Publications/cade07.ps
author Christian Urban <christian.urban@kcl.ac.uk>
Thu, 27 Oct 2022 08:17:23 +0100
changeset 620 dc3e7e763f6b
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   593
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   594
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   595
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   596
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   597
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   598
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   599
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   600
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   601
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   602
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   603
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   604
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   605
07E00000003F0FE00000003F0FC00000003F1FC00000003F1FC00000007F1F800000007F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   606
3F800000007F3F800000007F3F800000007F7F00000000FE7F00000000FE7F00000000FE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   607
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   608
FE00000007F0FE00000007E0FE0000000FE07E0000000FC07E0000001F807E0000001F80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   609
7E0000003F003F0000007E003F000000FC003F000000F8001F800001F0000F800003E000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   610
0FC00007C00007C0001F800003E0003E000001F800FC0000007E07F00000003FFF800000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   611
0007FC000000303775B43B>I<0007FFFFFFC000000FFFFFFFF800000FFFFFFFFC000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   612
3F8001FE0000003F80003F0000003F80001F8000003F00001FC000003F00000FC000007F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   613
00000FC000007F00000FE000007E00000FE000007E00000FE00000FE00000FE00000FE00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   614
001FC00000FC00001FC00000FC00001FC00001FC00001F800001FC00003F800001F80000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   615
3F000001F800007E000003F80000FE000003F80000FC000003F00003F8000003F00007E0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   616
000007F0003FC0000007FFFFFF00000007FFFFF800000007E000000000000FE000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   617
000FE000000000000FC000000000000FC000000000001FC000000000001FC00000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   618
1F8000000000001F8000000000003F8000000000003F8000000000003F0000000000003F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   619
0000000000007F0000000000007F0000000000007E0000000000007E000000000000FE00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   620
0000000000FE000000000000FC000000000001FC00000000007FFFF000000000FFFFF000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   621
000000FFFFF00000000033337CB234>I<0007FFFFFE0000000FFFFFFFC000000FFFFFFF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   622
F00000003F8007F80000003F8001FC0000003F80007E0000003F00007F0000003F00003F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   623
0000007F00003F0000007F00003F8000007E00003F8000007E00003F800000FE00003F80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   624
0000FE00007F000000FC00007F000000FC00007F000001FC0000FE000001FC0000FC0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   625
01F80001FC000001F80001F8000003F80003F0000003F8000FC0000003F0001F80000003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   626
F000FE00000007FFFFF000000007FFFFC000000007E003E000000007E001F80000000FE0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   627
00FC0000000FE0007C0000000FC0007E0000000FC0007E0000001FC0007E0000001FC000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   628
7E0000001F80007E0000001F80007E0000003F8000FE0000003F8000FE0000003F0000FE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   629
0000003F0000FE0000007F0001FE0000007F0001FC0000007E0001FC0000007E0001FC01
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   630
C000FE0001FC03C000FE0001FC038000FC0001FC038001FC0001FC07807FFFF000FC0700
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   631
FFFFF000FE0E00FFFFF0007E1C00000000001FF8000000000007E00032357BB238>82
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   632
D<000001FC018000000FFF038000003FFFC78000007E07EF800001F801FF000003F000FF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   633
000003E0007F000007C0007F00000F80003E00001F80003E00001F00003E00003F00003E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   634
00003E00003C00003E00003C00003E00003C00007E00003C00007E00003800007E000038
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   635
00007E00000000007F00000000007F00000000003F80000000003FE0000000003FFE0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   636
00001FFFC00000000FFFF800000007FFFC00000001FFFE000000007FFF000000000FFF80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   637
00000000FF80000000003F80000000001FC0000000000FC0000000000FC0000000000FC0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   638
000000000FC0000E00000FC0000E00000FC0001E00000F80001C00000F80001C00000F80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   639
001C00001F80003C00001F00003C00001F00003E00003E00003E00007C00007E00007C00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   640
007F0000F800007F8001F000007FC007E00000F3F80FC00000F0FFFF000000E03FFC0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   641
00C00FF000000029377AB42B>I<03FFFFFFFFFFC007FFFFFFFFFFC007FFFFFFFFFF8007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   642
F800FC003F800FC001FC001F800F8001FC000F800F0001F8000F801E0001F80007001E00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   643
03F80007001C0003F80007003C0003F0000F003C0003F0000F00380007F0000E00780007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   644
F0000E00700007E0000E00700007E0000E0070000FE0001E00F0000FE0001C0000000FC0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   645
00000000000FC000000000001FC000000000001FC000000000001F8000000000001F8000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   646
000000003F8000000000003F8000000000003F0000000000003F0000000000007F000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   647
0000007F0000000000007E0000000000007E000000000000FE000000000000FE00000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   648
0000FC000000000000FC000000000001FC000000000001FC000000000001F80000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   649
01F8000000000003F8000000000003F8000000000003F0000000000003F0000000000007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   650
F0000000000007F0000000000007E000000000000FF0000000001FFFFFF00000003FFFFF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   651
F00000003FFFFFF0000000323374B237>I<0003F000000FF800003E1C60007C0FF000F8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   652
07F001F007F003E007F007E003E00FC003E00FC003E01F8007E01F8007C03F0007C03F00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   653
07C03F000FC07F000F807E000F807E000F807E001F80FE001F00FC001F00FC001F06FC00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   654
3F07FC003E0FFC003E0EFC007E0E7C007E1E7C00FE1C7C01FC1C3C03FC3C3E07BE381F0E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   655
1E7807FC0FF001F003C0202278A027>97 D<007E00000FFE00001FFE00001FFC000000FC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   656
000000FC000000FC000000F8000000F8000001F8000001F8000001F0000001F0000003F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   657
000003F0000003E0000003E0000007E0000007E0000007C3E00007CFF8000FDC3E000FF8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   658
1F000FF00F000FE00F801FC00F801F800F801F800FC01F000FC03F000FC03F000FC03E00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   659
0FC03E000FC07E001FC07E001F807C001F807C001F807C003F80FC003F00F8003F00F800
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   660
3F00F8007E00F8007E00F800FC00F800FC007801F8007801F0007803E0003C07C0003C0F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   661
80001E1F00000FFC000003F000001A3578B323>I<0000FC000007FF00001F0780003E03
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   662
C000FC01C001F803C003F007C007E00FC007C00FC00FC00FC01F8007001F8000003F0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   663
003F0000003F0000007F0000007E0000007E0000007E000000FE000000FC000000FC0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   664
00FC000000FC0000007C0000C07C0001E07C0001E07C0003C03E000F803E001F001F007C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   665
000F81F00003FFC00000FE00001B2278A023>I<0000000FC0000003FFC0000003FFC000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   666
0003FF800000001F800000001F800000001F800000001F000000001F000000003F000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   667
003F000000003E000000003E000000007E000000007E000000007C000000007C00000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   668
FC00000000FC000003F0F800000FF8F800003E1DF800007C0FF80000F807F00001F007F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   669
0003E007F00007E003F0000FC003E0000FC003E0001F8007E0001F8007E0003F0007C000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   670
3F0007C0003F000FC0007F000FC0007E000F80007E000F80007E001F8000FE001F8000FC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   671
001F0000FC001F0600FC003F0700FC003F0F00FC003E0E00FC007E0E007C007E1E007C00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   672
FE1C007C01FC1C003C03FC3C003E07BE38001F0E1E780007FC0FF00001F003C000223578
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   673
B327>I<0003F800000FFE00003E0F0000F8078001F0038003E0038007C003800FC00380
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   674
1F8003801F8007803F0007003F000F007E003E007E03F8007FFFE000FFFE0000FC000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   675
FC000000FC000000FC000000F8000000F8000000F8000000F8000000F8000180F80003C0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   676
F80003C07C0007807C001F003C003E001E00F8000F03E00007FF800001FC00001A2277A0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   677
23>I<0000001F000000007FC0000000F0E0000001F0F0000003E3F0000003E3F0000007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   678
C3F0000007C3E0000007C1C000000FC00000000F800000000F800000000F800000000F80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   679
0000001F800000001F000000001F000000001F000000001F000000003F000000003E0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   680
001FFFFE00001FFFFE00001FFFFE0000007E000000007C000000007C000000007C000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   681
007C00000000FC00000000F800000000F800000000F800000000F800000000F800000001
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   682
F800000001F000000001F000000001F000000001F000000003F000000003E000000003E0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   683
00000003E000000003E000000007E000000007C000000007C000000007C00000000FC000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   684
00000FC00000000F800000000F800000000F800000001F800000001F000000001F000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   685
001F000000003F000000003E000000383E0000007E3C0000007E3C000000FE78000000FC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   686
78000000F8F000000078E00000003FC00000000F00000000244582B418>I<00003F0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   687
00FF800003E1E60007C0FF000F807F001F007F003E007F007E003F00FC003E00FC003E01
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   688
F8007E01F8007E03F0007C03F0007C03F000FC07F000FC07E000F807E000F807E001F807
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   689
E001F80FC001F00FC001F00FC003F007C003F007C003E007C007E007C00FE007C01FE003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   690
E03FC001E07FC001F0FFC0007FCFC0001F0F8000000F8000001F8000001F8000001F0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   691
001F0000003F0000003E0038003E007E007E007E00FC00FE00F800FC01F0007803E0007C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   692
0F80001FFF000007F8000020317CA023>I<000FC0000003FFC0000003FFC0000003FF80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   693
0000001F800000001F800000001F800000001F000000001F000000003F000000003F0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   694
00003E000000003E000000007E000000007E000000007C000000007C00000000FC000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   695
00FC00000000F83F800000F8FFE00001FBE0F00001FF80F80001FF00780001FE007C0003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   696
FC007C0003F8007C0003F0007C0003F0007C0007E000FC0007E000F80007C000F80007C0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   697
00F8000FC001F8000FC001F0000F8001F0000F8001F0001F8003F0001F8003E0001F0007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   698
E0001F0007C0C03F0007C1E03F000FC1C03E000F81C03E000F81C07E000F83C07E000F03
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   699
807C000F07807C000F0700FC000F0E00FC000F1E00F80007F800700001F00023357BB327
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   700
>I<0001800007E00007E0000FE00007C000038000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   701
000000000000000000000000000000000001F00003FC000F1E000E1E001C1E003C1E0038
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   702
1E00783E00703E00703E00707E00F07C0060FC0000F80000F80001F80001F00001F00003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   703
F00003E00003E00007E0C007C1E00FC1C00F81C00F81C00F83C00F03800F07800F07000F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   704
0E000F1E0007F80001F00013337AB118>I<000FC00001FFC00003FFC00003FF8000001F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   705
8000001F8000001F8000001F0000001F0000003F0000003F0000003E0000003E0000007E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   706
0000007E0000007C0000007C000000FC000000FC000000F8007800F801FE01F8078F01F8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   707
0E0F01F01C3F01F0383F03F0703F03F0E03E03E1C01C03E3800007E7000007EE000007DC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   708
000007F800000FF800000FFF00000F9FC0000F83F0001F81F0001F80F8001F00F8001F00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   709
F80C3F00F81E3F00F81C3E00F81C3E00F81C7E00F83C7E00F8387C00F8387C00F878FC00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   710
7870FC0078E0F8003FC070000F8020357BB323>107 D<003F07FF0FFF0FFE007E007E00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   711
7E007C007C00FC00FC00F800F801F801F801F001F003F003F003E003E007E007E007C007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   712
C00FC00FC00F800F801F801F801F001F003F003F003E003E007E007E007C007C18FC1CFC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   713
3CF838F838F878F870F070F0F0F8E079E03FC00F00103579B314>I<03C003F8007F0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   714
0FF00FFE01FFC0001E783C1F07C1E0001C7CF00F8F01F0003C3DE0079E00F000383FC007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   715
FC00F800387F8007F800F800707F0007F000F800707F0007E000F800707E0007E000F800
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   716
F0FC000FC001F800E0FC000FC001F00060F8000F8001F00000F8000F8001F00001F8001F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   717
8003F00001F8001F8003E00001F0001F0003E00001F0001F0003E00003F0003F0007E000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   718
03F0003F0007C00003E0003E000FC00003E0003E000F818007E0007E000F83C007E0007E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   719
001F838007C0007C001F038007C0007C001F03800FC000FC001F07800FC000FC003E0700
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   720
0F8000F8003E0F000F8000F8001E0E001F8001F8001E1C001F8001F8001E3C001F0001F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   721
000FF0000E0000E00003E0003A227AA03F>I<03C007F0000FF01FFC001E787C1E001C7C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   722
F01F003C3DE00F00383FC00F80387F800F80787F000F80707E000F80707E000F80F0FC00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   723
1F80E0FC001F0060F8001F0000F8001F0001F8003F0001F8003E0001F0003E0001F0003E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   724
0003F0007E0003F0007C0003E000FC0003E000F81807E000F83C07E001F83807C001F038
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   725
07C001F0380FC001F0780FC001E0700F8001E0F00F8001E0E01F8001E1C01F8001E3C01F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   726
0000FF000E00003E0026227AA02B>I<0000FC000007FF00001F07C0003E03E000FC01F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   727
01F801F003F000F807E000F807C000F80FC000F81F8000FC1F8000FC3F0000FC3F0000FC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   728
3F0001FC7F0001F87E0001F87E0001F87E0003F8FE0003F0FC0003F0FC0003F0FC0007E0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   729
FC0007E07C000FC07C000F807C001F807C003F003E007E003E00FC001F01F0000F83E000
Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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  1900
FC0007E0003F0000FC0007E0003F0000FC000FE0007F0001FC000FE0007E0001F8000FC0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1901
007E0001F8000FC000FE0001F8001FC000FC0003F8001FC000FC0003F0001F8001FC1C03
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1902
F0001F8001F81C03F0003F8001F83C07F0003F8003F83807E0003F0003F03807E0003F00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1903
03F03807E0007F0003F0700FE0007F0003E0700FC0007E0003E0F00FC0007E0003E0E00F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1904
C000FE0003E1C01FC000FE0001E3C01F8000FC0000FF000700003800003C003E2679A444
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1905
>I<01E000FE000007F803FF80000E3C0F07C0001E3E3C03E0001C1F7803F000383FF001
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1906
F000383FE001F000783FC001F000703FC001F800703F8001F800703F0003F000F07F0003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1907
F000E07E0003F000E07E0003F000007E0007F00000FE0007E00000FC0007E00000FC0007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1908
E00000FC000FE00001FC000FC00001F8000FC00001F8001FC00001F8001F800003F8001F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1909
800003F0003F838003F0003F038003F0003F078007F0007F070007E0007E070007E0007E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1910
070007E0007E0E000FE0007C0E000FC0007C1E000FC0007C1C000FC0007C38001FC0003C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1911
78001F80001FE000070000078000292679A42F>I<00007F000003FFC0000FC1F0001F00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1912
F8007E007C00FC007C01F8007E03F0003E07F0003F07E0003F0FE0003F1FC0003F1FC000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1913
3F3F80003F3F80007F7F80007F7F00007F7F00007F7F0000FFFF0000FFFE0000FEFE0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1914
FEFE0001FEFE0001FCFC0001FCFC0003F8FC0003F8FC0007F0FC0007E0FC000FE07C000F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1915
C07E001F803E003F003E007E001F00F8000F83F00003FFC00000FE0000202677A42A>I<
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1916
00078007C000001FE03FF000003CF0787C000038F8E03E0000787FC03E0000707F801F00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1917
0070FF001F0000F0FE001F8000E0FE001F8000E0FC001F8001E1FC001F8001C1FC001F80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1918
01C1F8001F8001C1F8001F800003F8003F800003F8003F800003F0003F800003F0003F80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1919
0007F0007F800007F0007F800007E0007F000007E0007F00000FE000FF00000FE000FE00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1920
000FC000FE00000FC001FC00001FC001FC00001FC001F800001F8003F800001F8003F000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1921
003F8007E000003FC00FC000003FC00F8000003FE01F0000007FE03E0000007F70FC0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1922
007E3FF00000007E0F80000000FE0000000000FE0000000000FC0000000000FC00000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1923
01FC0000000001FC0000000001F80000000001F80000000003F80000000003F800000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1924
03F00000000007F000000000FFFFC0000000FFFFC0000000FFFFC0000000293580A42A>
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1925
I<0000F8030007FE07001F871F003E03BF007C03FE00F801FE01F801FE03F000FE07E000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1926
FC0FE000FC0FC000FC1FC001FC1FC001F83F8001F83F8001F87F8003F87F0003F07F0003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1927
F07F0003F0FF0007F0FE0007E0FE0007E0FE0007E0FE000FE0FC000FC0FC000FC0FC000F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1928
C0FC001FC0FC001F80FC003F80FC003F807C007F807C00FF003E01FF003E03BF001F0F7F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1929
0007FE7E0001F07E0000007E000000FE000000FC000000FC000000FC000001FC000001F8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1930
000001F8000001F8000003F8000003F0000007F00001FFFFC001FFFFC001FFFFC0203577
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1931
A426>I<03C003F0000FF01FFC001E783C0F001C7C700F003C3EE03F80383FC03F80387F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1932
803F80787F803F00707F003F00707F001C00F07E000000E0FE000000E0FC000000E0FC00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1933
000000FC00000001FC00000001F800000001F800000001F800000003F800000003F00000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1934
0003F000000003F000000007F000000007E000000007E000000007E00000000FE0000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1935
0FC00000000FC00000000FC00000001FC00000001F800000001F800000001F800000003F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1936
800000003F000000000E00000000212679A423>I<0000FE000007FF80000F83C0003E00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1937
E0007C00F00078007000F800F001F803F001F003F001F003F001F003E003F001C003F800
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1938
0003FC000003FFC00001FFF80001FFFE0000FFFF00007FFF80003FFF80000FFFC00000FF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1939
C000003FC000001FC000000FC03E000FC07E000FC0FE000F80FE000F80FE000F80FC001F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1940
00E0001F00F0003E0070007C003800F8001E03E0000FFFC00001FE00001C267AA422>I<
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1941
0003800007C0000FC0000FC0000FC0000FC0001FC0001F80001F80001F80003F80003F00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1942
003F00003F00007F00007E007FFFFF7FFFFFFFFFFF00FC0000FC0000FC0001FC0001F800
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1943
01F80001F80003F80003F00003F00003F00007F00007E00007E00007E0000FE0000FC000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1944
0FC0000FC0001FC0001F801C1F801C1F803C3F80383F00783F00703F00F03F00E03F01C0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1945
3E03C01F07800F0F0007FC0001F000183579B31C>I<00F800000003FE0001C0078F0003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1946
E00E0F8007E01E0F8007E01C0F8007E0380F800FE0381F800FE0781F800FC0701F800FC0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1947
703F801FC0F03F001FC0E03F001F80E07F001F80007E003F80007E003F8000FE003F0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1948
FC003F0000FC007F0001FC007F0001F8007E0001F8007E0001F800FE0003F800FE0003F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1949
00FC0E03F000FC0E03F001FC1E03F001FC1C03F001F81C03E001F81C03E001F83C03F003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1950
F83803F007F83801F007F07001F01EF8F000F83C78E0003FF03FC0000FC00F00272679A4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1951
2D>I<00F0000E0003FC003F00071E007F800E1F007F801C1F007F803C1F007F80381F00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1952
3F80383F001F80703F000F80703F000F80707F000F80F07E000F00E07E000700E0FE0007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1953
0000FC000F0000FC000E0001FC000E0001F8000E0001F8001E0003F8001C0003F0001C00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1954
03F0001C0003F0003C0007F000380007E000380007E000700007E000700007E000700007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1955
E000E00007E000E00007E001C00007E003C00003E003800003F007000001F00E000000F8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1956
3C0000007FF80000000FC00000212679A426>I<00F0000000070003FC0003801F80071E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1957
0007C03FC00E1F000FC03FC01C1F000FC03FC03C1F000FC03FC0381F001FC01FC0383F00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1958
1F800FC0703F001F8007C0703F001F8007C0707F003F8007C0F07E003F800780E07E003F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1959
000380E0FE003F00038000FC007F00078000FC007F00070001FC007E00070001F8007E00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1960
070001F800FE000F0003F800FE000E0003F000FC000E0003F000FC000E0003F000FC001E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1961
0007F001FC001C0007E001F8001C0007E001F8003C0007E001F800380007E001F8003800
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1962
07E001F800780007E001F800700007E003F800F00007E003F800E00003E007F801E00003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1963
F00FFC03C00001F01E7C07800000FC3C3E0F0000003FF81FFE0000000FE003F000003226
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1964
79A437>I<0007E007C0001FF81FF800787C383C00F03E703C01E01EE0FE03C01FE0FE03
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1965
801FC0FE07001FC0FC0F001F80FC0E001F80700E003F80001E003F00001C003F00001C00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1966
3F000000007F000000007F000000007E000000007E00000000FE00000000FE00000000FC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1967
00000000FC00000001FC00000001FC00000001F800700001F800700003F800F00003F800
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1968
E01C03F000E07E03F001E07E07F001C0FE07F00380FE0FF00780FE0EF00F00781CF81E00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1969
78387C3C003FF03FF00007C00FC00027267CA427>I<00F000000003FC0001C0071E0003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1970
E00E1F0007E01C1F0007E03C1F0007E0381F000FE0383F000FC0703F000FC0703F000FC0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1971
707F001FC0F07E001F80E07E001F80E0FE001F8000FC003F8000FC003F0001FC003F0001
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1972
F8003F0001F8007F0003F8007E0003F0007E0003F0007E0003F000FE0007F000FC0007E0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1973
00FC0007E000FC0007E001FC0007E001F80007E001F80007E001F80007E003F80007E003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1974
F00007E007F00003E00FF00003F01FF00001F87FE000007FF7E000001FC7E00000000FE0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1975
0000000FC00000000FC00000001FC0003F001F80007F003F80007F003F00007F007E0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1976
7F007C00007E00FC00007001F800007003E000003807C000003C1F8000000FFE00000003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1977
F0000000233679A428>I E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1978
%EndDVIPSBitmapFont
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1979
%DVIPSBitmapFont: Ft cmbx10 10 46
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1980
/Ft 46 122 df<000003FFC00000007FFFF0000003FFFFFC00000FFF00FE00003FF8003F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1981
00007FE000FF8000FFC001FF8001FFC001FF8001FF8001FF8003FF8003FFC003FF0001FF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1982
8003FF0001FF8003FF0001FF8003FF0000FF0003FF00007E0003FF0000000003FF000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1983
0003FF0000000003FF0000000003FF0000000003FF003FFFC0FFFFFFFFFFC0FFFFFFFFFF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1984
C0FFFFFFFFFFC0FFFFFFFFFFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1985
C003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1986
C003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1987
C003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1988
C003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1989
C003FF0000FFC0FFFFFC3FFFFFFFFFFC3FFFFFFFFFFC3FFFFFFFFFFC3FFFFF303A7EB935
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1990
>12 D<00001C00003C0000F80001F00003E00007E0000FC0001F80001F00003F00007E00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1991
00FE0000FC0001FC0001F80003F80003F80007F00007F0000FF0000FE0001FE0001FE000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1992
1FC0003FC0003FC0003FC0003FC0007F80007F80007F80007F80007F8000FF8000FF8000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1993
FF8000FF8000FF8000FF8000FF8000FF8000FF8000FF8000FF8000FF8000FF8000FF8000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1994
FF8000FF8000FF80007F80007F80007F80007F80007F80003FC0003FC0003FC0003FC000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1995
1FC0001FE0001FE0000FE0000FF00007F00007F00003F80003F80001F80001FC0000FC00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1996
00FE00007E00003F00001F00001F80000FC00007E00003E00001F00000F800003C00001C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1997
165377BD25>40 D<E00000F000007C00003E00001F00001F80000FC00007E00003E00003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1998
F00001F80001FC0000FC0000FE00007E00007F00007F00003F80003F80003FC0001FC000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1999
1FE0001FE0000FE0000FF0000FF0000FF0000FF00007F80007F80007F80007F80007F800
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2000
07FC0007FC0007FC0007FC0007FC0007FC0007FC0007FC0007FC0007FC0007FC0007FC00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2001
07FC0007FC0007FC0007FC0007FC0007F80007F80007F80007F80007F8000FF0000FF000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2002
0FF0000FF0000FE0001FE0001FE0001FC0003FC0003F80003F80007F00007F00007E0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2003
FE0000FC0001FC0001F80003F00003E00007E0000FC0001F80001F00003E00007C0000F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2004
0000E0000016537BBD25>I<0F803FE07FF07FF0FFF8FFF8FFF8FFF8FFF87FF07FF03FE0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2005
0F800D0D798C1B>46 D<00001E000000003E00000000FE00000007FE0000003FFE0000FF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2006
FFFE0000FFFFFE0000FFFFFE0000FFCFFE0000000FFE0000000FFE0000000FFE0000000F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2007
FE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2008
0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2009
00000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2010
000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2011
0FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2012
FE0000000FFE0000000FFE00007FFFFFFF807FFFFFFF807FFFFFFF807FFFFFFF80213779
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2013
B630>49 D<000FFC0000007FFFC00001FFFFF00007FFFFFC000FF03FFF001F800FFF803F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2014
0003FFC07F0003FFC07FC001FFE0FFE000FFF0FFF000FFF0FFF000FFF0FFF0007FF8FFF0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2015
007FF8FFF0007FF8FFF0007FF87FE0007FF83FC0007FF80F00007FF80000007FF8000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2016
FFF0000000FFF0000000FFE0000001FFE0000001FFC0000003FF80000003FF00000007FE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2017
00000007FC0000000FF80000001FF00000003FE00000007F800000007F00000000FE0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2018
0001F800000003F000780007E00078000FC00078001F800078003E0000F8007C0000F000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2019
F80000F001F00001F003FFFFFFF003FFFFFFF007FFFFFFF00FFFFFFFF01FFFFFFFF03FFF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2020
FFFFF07FFFFFFFE0FFFFFFFFE0FFFFFFFFE0FFFFFFFFE0FFFFFFFFE025377BB630>I<00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2021
03FF0000001FFFF000007FFFFC0001FC07FF0003F003FF8007E001FFC007C000FFE00FF0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2022
00FFE00FFC00FFF01FFC00FFF01FFE00FFF01FFE00FFF01FFE00FFF01FFE00FFF01FFE00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2023
FFF00FFC00FFE00FFC00FFE003F001FFE0000001FFC0000003FF80000003FF00000007FE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2024
0000000FFC0000003FF000000FFFC000000FFF0000000FFFF000000007FE00000001FF80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2025
000000FFC0000000FFE00000007FF00000007FF80000007FFC0000003FFC0000003FFC00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2026
00003FFE1FC0003FFE3FE0003FFE7FF0003FFEFFF8003FFEFFF8003FFEFFF8003FFEFFF8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2027
003FFEFFF8003FFCFFF8003FFCFFF0007FF87FF0007FF87FC000FFF03F8000FFE01FC001
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2028
FFC00FFC07FF8007FFFFFF0001FFFFFC00007FFFF0000007FF000027387CB630>I<0000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2029
0007C0000000000FC0000000000FC0000000001FC0000000003FC0000000007FC0000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2030
00FFC000000000FFC000000001FFC000000003FFC000000007FFC00000000FFFC0000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2031
0FFFC00000001EFFC00000003CFFC00000007CFFC0000000F8FFC0000000F0FFC0000001
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2032
E0FFC0000003C0FFC0000007C0FFC000000F80FFC000000F00FFC000001E00FFC000003C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2033
00FFC000007C00FFC00000F800FFC00000F000FFC00001E000FFC00003C000FFC00007C0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2034
00FFC0000F8000FFC0000F0000FFC0001E0000FFC0003C0000FFC0007C0000FFC000F800
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2035
00FFC000FFFFFFFFFF80FFFFFFFFFF80FFFFFFFFFF80FFFFFFFFFF80000001FFC0000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2036
01FFC000000001FFC000000001FFC000000001FFC000000001FFC000000001FFC0000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2037
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4051
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4052
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4053
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4054
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4057
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4058
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4059
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4060
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4061
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4062
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4063
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4064
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4065
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4066
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4067
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4069
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4070
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4071
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4072
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
  4075
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4080
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4081
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4085
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4087
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4090
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4091
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4093
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4094
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4096
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4097
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4098
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4099
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4100
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4101
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4102
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4103
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4106
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4108
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4109
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4114
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4115
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4116
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4118
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4120
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4121
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4122
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4123
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4124
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4125
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4126
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4127
F00003F00003F00003F00003F00003F00003F00003F00003F00003F00003F00003F00003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4128
F00003F00003F00003F00003F00003F00003F00003F00003F00003F00003F00003F00003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4129
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4130
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4131
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4132
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4133
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4134
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4135
C003F00007E0000FC003F00007E0000FC003F00007E0000FC003F00007E0000FC003F000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4139
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4140
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4141
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4142
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4143
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4144
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4145
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4146
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4147
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4150
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4152
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4153
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4154
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4155
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4156
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4157
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4158
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4159
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4161
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4162
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4163
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4164
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
  4627
y Fn(M)29 b Fm(\000)-13 b(!)2189 4714 y Fo(1)2149 4698
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4628
y Fm(\000)f(!)22 b Fn(M)2376 4666 y Fl(0)2475 4698 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4629
Fn(N)30 b Fm(\000)-13 b(!)2635 4714 y Fo(1)2594 4698
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4630
y Fm(\000)g(!)21 b Fn(N)2808 4666 y Fl(0)p 1817 4724
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4631
1215 4 v 1817 4800 a Fk(app)5 b Fw(\()p Fk(lam)g Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4632
Fn(y)s(:M)j Fw(\))p Fn(;)13 b(N)8 b Fw(\))22 b Fm(\000)-13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4633
b(!)2524 4816 y Fo(1)2483 4800 y Fm(\000)g(!)21 b Fn(M)2710
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4634
4769 y Fl(0)2733 4800 y Fw([)p Fn(y)j Fw(:=)d Fn(N)2987
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4635
4769 y Fl(0)3010 4800 y Fw(])3073 4746 y(One)3210 4754
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4636
y Fx(4)3307 4634 y Fw(\(1\))523 4924 y Fz(The)28 b(substitutivit)n(y)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4637
(prop)r(ert)n(y)e(states:)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4638
%%Page: 2 2
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4639
TeXDict begin 2 1 bop Black 523 232 a Fw(2)237 b(Christian)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4640
b(Urban,)e(Stefan)h(Berghofer,)i(and)d(Mic)n(hael)i(Norrish)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4641
Black 523 448 a Ft(Lemma.)e Fz(If)j Fr(M)k Fp(\000)-15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4642
b(!)1153 466 y Fo(1)1108 448 y Fp(\000)g(!)24 b Fr(M)1355
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4643
418 y Fj(0)1405 448 y Fz(and)k Fr(N)k Fp(\000)-15 b(!)1739
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4644
466 y Fo(1)1694 448 y Fp(\000)g(!)24 b Fr(N)1927 418
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4645
y Fj(0)1950 448 y Fz(,)j(then)h Fr(M)9 b Fz([)p Fr(x)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4646
b Fz(:=)e Fr(N)9 b Fz(])23 b Fp(\000)-14 b(!)2679 466
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4647
y Fo(1)2633 448 y Fp(\000)g(!)23 b Fr(M)2880 418 y Fj(0)2903
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4648
448 y Fz([)p Fr(x)h Fz(:=)e Fr(N)3183 418 y Fj(0)3207
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4649
448 y Fz(].)523 570 y(In)32 b([2],)g(the)g(pro)r(of)f(of)h(this)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4650
(lemma)g(pro)r(ceeds)f(b)n(y)h(an)f(induction)h(o)n(v)n(er)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4651
(de\014nition)g(of)523 670 y Fr(M)g Fp(\000)-15 b(!)709
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4652
687 y Fo(1)664 670 y Fp(\000)g(!)24 b Fr(M)911 639 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4653
Fj(0)934 670 y Fz(.)j(Though)g(Barendregt)f(do)r(es)h(not)h(ac)n(kno)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4654
(wledge)d(the)j(fact)f(explicitly)-7 b(,)28 b(there)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4655
769 y(are)37 b(t)n(w)n(o)g(places)h(in)g(his)g(pro)r(of)f(where)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4656
(v)-5 b(ariable)37 b(con)n(v)n(en)n(tion)g(is)h(used.)g(In)g(case)f(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4657
523 869 y(rule)23 b(One)833 881 y Fy(2)870 869 y Fz(,)h(for)f(example,)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4658
g(Barendregt)f(writes)h(\(sligh)n(tly)h(c)n(hanged)e(to)i(conform)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4659
(with)j(the)523 968 y(syn)n(tax)i(w)n(e)g(shall)g(emplo)n(y)g(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4660
Fr(\025)p Fz(-terms\):)523 1112 y Ft(Case)20 b Fz(One)888
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4661
1124 y Fy(2)925 1112 y Fz(.)43 b Fr(M)32 b Fp(\000)-15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4662
b(!)1177 1130 y Fo(1)1132 1112 y Fp(\000)g(!)24 b Fr(M)1379
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4663
1082 y Fj(0)1422 1112 y Fz(is)33 b Fs(lam)7 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4664
Fr(y)s(:P)12 b Fz(\))23 b Fp(\000)-14 b(!)1942 1130 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4665
Fo(1)1897 1112 y Fp(\000)f(!)24 b Fs(lam)6 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4666
Fr(y)s(:P)2355 1082 y Fj(0)2379 1112 y Fz(\))34 b(and)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4667
b(is)g(a)f(direct)h(consequence)523 1212 y(of)28 b Fr(P)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4668
b Fp(\000)-14 b(!)781 1230 y Fo(1)735 1212 y Fp(\000)g(!)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4669
b Fr(P)958 1182 y Fj(0)981 1212 y Fz(.)k(By)g(induction)h(h)n(yp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4670
(othesis)e(one)h(has)g Fr(P)12 b Fz([)p Fr(x)24 b Fz(:=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4671
Fr(N)9 b Fz(])23 b Fp(\000)-14 b(!)2711 1230 y Fo(1)2666
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4672
1212 y Fp(\000)f(!)24 b Fr(P)12 b Fz([)p Fr(x)25 b Fz(:=)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4673
Fr(N)3170 1182 y Fj(0)3193 1212 y Fz(].)29 b(But)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4674
1311 y(then)j Fs(lam)7 b Fz(\()p Fr(y)s(:P)12 b Fz([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4675
Fr(x)30 b Fz(:=)f Fr(N)9 b Fz(]\))30 b Fp(\000)-14 b(!)1470
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4676
1329 y Fo(1)1424 1311 y Fp(\000)g(!)30 b Fs(lam)7 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4677
Fr(y)s(:P)1890 1281 y Fj(0)1913 1311 y Fz([)p Fr(x)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4678
b Fz(:=)f Fr(N)2206 1281 y Fj(0)2229 1311 y Fz(]\),)j(i.e.)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4679
Fr(M)9 b Fz([)p Fr(x)30 b Fz(:=)f Fr(N)9 b Fz(])30 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4680
Fp(\000)-15 b(!)2986 1329 y Fo(1)2941 1311 y Fp(\000)g(!)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4681
b Fr(M)3194 1281 y Fj(0)3217 1311 y Fz([)p Fr(x)g Fz(:=)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4682
1411 y Fr(N)599 1381 y Fj(0)622 1411 y Fz(].)2682 b Fp(u)-55
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4683
b(t)523 1546 y Fz(Ho)n(w)n(ev)n(er,)26 b(the)i(last)f(step)h(in)g(this)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4684
f(case)g(only)g(w)n(orks)f(if)i(one)g(kno)n(ws)e(that)1249
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4685
1694 y Fk(lam)6 b Fw(\()p Fn(y)s(:P)11 b Fw([)p Fn(x)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4686
b Fw(:=)i Fn(N)8 b Fw(]\))24 b(=)f Fk(lam)5 b Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4687
Fn(y)s(:P)11 b Fw(\)[)p Fn(x)21 b Fw(:=)g Fn(N)8 b Fw(])69
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4688
b(and)1205 1809 y Fk(lam)5 b Fw(\()p Fn(y)s(:P)1484 1777
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4689
y Fl(0)1506 1809 y Fw([)p Fn(x)21 b Fw(:=)g Fn(N)1763
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4690
1777 y Fl(0)1786 1809 y Fw(]\))j(=)f Fk(lam)5 b Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4691
Fn(y)s(:P)2223 1777 y Fl(0)2245 1809 y Fw(\)[)p Fn(x)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4692
b Fw(:=)g Fn(N)2532 1777 y Fl(0)2555 1809 y Fw(])523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4693
1961 y Fz(whic)n(h)31 b(only)g(holds)g(when)g(the)h(b)r(ound)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4694
b(ariable)30 b Fr(y)k Fz(is)d(not)h(equal)e(to)h Fr(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4695
Fz(,)h(and)f(not)h(free)f(in)523 2060 y Fr(N)40 b Fz(and)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4696
b Fr(N)870 2030 y Fj(0)894 2060 y Fz(.)h(These)f(assumptions)g(migh)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4697
(t)h(b)r(e)g(inferred)g(from)f(the)i(v)-5 b(ariable)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4698
b(con)n(v)n(en)n(tion,)523 2160 y(pro)n(vided)36 b(one)g(has)h(a)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4699
(formal)h(justi\014cation)g(for)f(this)h(con)n(v)n(en)n(tion.)f(Since)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4700
(one)f(usually)523 2260 y(assumes)29 b(that)i Fr(\025)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4701
Fz(-terms)f(are)f Fr(\013)p Fz(-equated,)i(one)f(migh)n(t)g(think)h(a)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4702
(simple)g(justi\014cation)h(for)523 2359 y(the)19 b(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4703
b(ariable)17 b(con)n(v)n(en)n(tion)g(is)i(along)e(the)i(lines)f(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4704
(one)f(can)g(alw)n(a)n(ys)f(rename)g(binders)h(with)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4705
2459 y(fresh)j(names.)g(This)g(is)g(ho)n(w)n(ev)n(er)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4706
Fs(not)29 b Fz(su\016cien)n(t)21 b(in)h(the)f(con)n(text)g(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4707
(inductiv)n(e)h(de\014nitions,)523 2559 y(b)r(ecause)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4708
b(there)f(rules)h(can)f(ha)n(v)n(e)g(the)h(same)f(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4709
b(ariable)32 b(o)r(ccurring)g(b)r(oth)h(in)g(binding)g(and)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4710
2658 y(non-binding)24 b(p)r(ositions.)f(In)i(rule)e(One)1760
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4711
2670 y Fy(4)1797 2658 y Fz(,)h(for)g(example,)f Fr(y)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4712
Fz(o)r(ccurs)c(in)i(binding)f(p)r(osition)g(in)523 2758
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4713
y(the)31 b(subterm)f Fs(lam)7 b Fz(\()p Fr(y)s(:M)i Fz(\),)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4714
b(and)f(in)h(the)f(subterm)h Fr(M)2234 2728 y Fj(0)2257
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4715
2758 y Fz([)p Fr(y)f Fz(:=)e Fr(N)2543 2728 y Fj(0)2566
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4716
2758 y Fz(])i(it)h(is)f(in)h(a)f Fs(non)6 b Fz(-binding)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4717
2857 y(p)r(osition.)28 b(Both)f(o)r(ccurrences)f(m)n(ust)i(refer)f(to)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4718
(the)h(same)f(v)-5 b(ariable)27 b(as)f(the)i(rule)1413
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4719
3013 y Fr(M)j Fp(\000)-14 b(!)1599 3031 y Fo(1)1553 3013
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4720
y Fp(\000)g(!)23 b Fr(M)1800 2983 y Fj(0)1906 3013 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4721
Fr(N)32 b Fp(\000)-14 b(!)2079 3031 y Fo(1)2033 3013
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4722
y Fp(\000)g(!)23 b Fr(N)2266 2983 y Fj(0)p 1195 3040
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4723
1311 4 v 1195 3119 a Fs(app)7 b Fz(\()p Fs(lam)g Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4724
Fr(z)t(:M)i Fz(\))p Fr(;)14 b(N)9 b Fz(\))23 b Fp(\000)-15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4725
b(!)1959 3137 y Fo(1)1914 3119 y Fp(\000)g(!)24 b Fr(M)2161
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4726
3089 y Fj(0)2184 3119 y Fz([)p Fr(y)h Fz(:=)e Fr(N)2460
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4727
3089 y Fj(0)2483 3119 y Fz(])2548 3064 y(One)2695 3028
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4728
y Fj(0)2695 3084 y Fy(4)523 3287 y Fz(leads)k(to)h(a)f(nonsensical)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4729
(reduction)h(relation.)648 3378 y(In)e(the)g(absence,)f(ho)n(w)n(ev)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4730
(er,)f(of)i(a)f(formal)g(justi\014cation)h(for)f(the)i(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4731
b(ariable)23 b(con)n(v)n(en)n(tion,)523 3470 y(Barendregt's)h(argumen)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4732
(t)g(considering)h(only)g(a)g(w)n(ell-c)n(hosen)f Fr(y)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4733
b Fz(seems)c(dubious,)g(b)r(ecause)523 3561 y(the)j(induction)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4734
(principle)g(that)f(comes)g(with)h(the)g(inductiv)n(e)g(de\014nition)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4735
(of)g Fp(\000)-15 b(!)3030 3579 y Fo(1)2985 3561 y Fp(\000)g(!)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4736
b Fz(is:)674 3708 y Fm(8)p Fn(M)t(:)42 b(P)24 b(M)d(M)674
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4737
3823 y Fm(8)p Fn(y)15 b(M)21 b(M)947 3791 y Fl(0)969
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4738
3823 y Fn(:)43 b(P)24 b(M)d(M)1283 3791 y Fl(0)1348 3823
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4739
y Fm(\))43 b Fn(P)23 b Fw(\()p Fk(lam)6 b Fw(\()p Fn(y)s(:M)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4740
Fw(\)\))k(\()p Fk(lam)5 b Fw(\()p Fn(y)s(:M)2275 3791
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4741
y Fl(0)2298 3823 y Fw(\)\))674 3938 y Fm(8)p Fn(M)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4742
b(M)893 3906 y Fl(0)929 3938 y Fn(N)h(N)1080 3906 y Fl(0)1103
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4743
3938 y Fn(:)43 b(P)23 b(M)f(M)1417 3906 y Fl(0)1478 3938
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4744
y Fm(^)38 b Fn(P)24 b(N)d(N)1791 3906 y Fl(0)1856 3938
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4745
y Fm(\))43 b Fn(P)23 b Fw(\()p Fk(app)6 b Fw(\()p Fn(M)t(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4746
b(N)8 b Fw(\)\))13 b(\()p Fk(app)5 b Fw(\()p Fn(M)2749
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4747
3906 y Fl(0)2771 3938 y Fn(;)13 b(N)2874 3906 y Fl(0)2897
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4748
3938 y Fw(\)\))674 4053 y Fm(8)p Fn(y)i(M)21 b(M)947
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4749
4021 y Fl(0)982 4053 y Fn(N)g(N)1133 4021 y Fl(0)1156
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4750
4053 y Fn(:)43 b(P)24 b(M)d(M)1470 4021 y Fl(0)1531 4053
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4751
y Fm(^)38 b Fn(P)24 b(N)d(N)1844 4021 y Fl(0)1910 4053
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4752
y Fm(\))42 b Fn(P)24 b Fw(\()p Fk(app)5 b Fw(\()p Fk(lam)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4753
Fw(\()p Fn(y)s(:M)j Fw(\))p Fn(;)13 b(N)8 b Fw(\)\))13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4754
b(\()p Fn(M)2903 4021 y Fl(0)2926 4053 y Fw([)p Fn(y)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4755
b Fw(:=)d Fn(N)3180 4021 y Fl(0)3203 4053 y Fw(]\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4756
674 4100 2581 4 v 1591 4168 a Fn(M)30 b Fm(\000)-13 b(!)1764
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4757
4184 y Fo(1)1723 4168 y Fm(\000)g(!)21 b Fn(N)51 b Fm(\))43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4758
b Fn(P)23 b(M)e(N)523 4327 y Fz(where)38 b(b)r(oth)h(cases)e(One)1348
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4759
4339 y Fy(2)1424 4327 y Fz(and)h(One)1744 4339 y Fy(4)1819
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4760
4327 y Fz(require)g(that)h(the)f(corresp)r(onding)f(implication)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4761
4426 y(holds)29 b(for)f Ft(all)g Fr(y)s Fz(,)h(not)g(just)g(the)g(ones)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4762
f(with)i Fr(y)e Fp(6)p Fz(=)c Fr(x)30 b Fz(and)e Fr(y)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4763
Fp(62)e Fr(F)12 b(V)18 b Fz(\()p Fr(N)t(;)c(N)2823 4396
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4764
y Fj(0)2847 4426 y Fz(\).)29 b(Nev)n(ertheless,)523 4526
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4765
y(w)n(e)e(will)g(sho)n(w)f(that)h(Barendregt's)e(apparen)n(tly)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4766
(dubious)i(step)g(can)f(b)r(e)i(giv)n(en)e(a)g(faithful,)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4767
4625 y(and)32 b(sound,)g(mec)n(hanisation.)f(Being)g(able)h(to)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4768
(restrict)f(the)i(argumen)n(t)e(in)h(general)e(to)i(a)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4769
4725 y(suitably)25 b(c)n(hosen)e(b)r(ound)i(v)-5 b(ariable)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4770
b(will,)h(ho)n(w)n(ev)n(er,)e(dep)r(end)i(on)f(the)i(form)e(of)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4771
(rules)f(in)523 4825 y(an)h(inductiv)n(e)g(de\014nition.)h(In)f(this)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4772
(pap)r(er)g(w)n(e)f(will)i(mak)n(e)e(precise)g(what)h(this)h(form)e(is)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4773
h(and)523 4924 y(will)j(sho)n(w)e(ho)n(w)h(the)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4774
b(ariable)26 b(con)n(v)n(en)n(tion)g(can)h(b)r(e)h(built)g(in)n(to)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4775
(the)g(induction)h(principle.)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4776
%%Page: 3 3
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4777
TeXDict begin 3 2 bop Black 1347 232 a Fw(Barendregt's)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4778
b(V)-6 b(ariable)26 b(Con)n(v)n(en)n(tion)f(in)h(Rule)f(Inductions)237
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4779
b(3)p Black 648 448 a Fz(The)27 b(in)n(teractions)f(b)r(et)n(w)n(een)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4780
(b)r(ound)g(and)f(free)g(o)r(ccurrences)f(of)h(v)-5 b(ariables,)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4781
b(and)g(their)523 548 y(consequences)19 b(for)g(obtaining)h(a)f(formal)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4782
h(argumen)n(t,)f(seem)h(to)f(often)i(b)r(e)f(o)n(v)n(erlo)r(ok)n(ed)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4783
(in)k(the)523 648 y(literature)i(when)h(claiming)f(that)h(pro)r(ofs)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4784
(b)n(y)h(rule)f(inductions)h(are)f(straigh)n(tforw)n(ard.)d(One)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4785
747 y(example)27 b(of)h(this)g(comes)f(with)h(a)f(w)n(eak)n(ening)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4786
(result)i(for)f(con)n(texts)g(in)h(the)g(simply-t)n(yp)r(ed)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4787
847 y Fr(\025)p Fz(-calculus.)648 939 y(W)-7 b(e)39 b(assume)e(t)n(yp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4788
(es)i(are)f(of)g(the)h(form)f Fr(T)94 b Fz(::=)82 b Fr(X)48
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4789
b Fp(j)41 b Fr(T)53 b Fp(!)41 b Fr(T)12 b Fz(,)38 b(and)g(that)h(t)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4790
(yping)523 1030 y(con)n(texts)27 b(\(\014nite)h(lists)f(of)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4791
b(ariable-t)n(yp)r(e)26 b(pairs\))g(are)h Fs(valid)37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4792
b Fz(if)28 b(no)f(v)-5 b(ariable)26 b(o)r(ccurs)g(t)n(wice.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4793
1121 y(The)i(t)n(yping)f(relation)g(can)g(then)h(b)r(e)g(de\014ned)g(b)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4794
n(y)f(the)h(rules)770 1274 y Fk(valid)7 b Fw(\()p Fn(\000)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4795
Fw(\))98 b(\()p Fn(x)9 b Fw(:)g Fn(T)i Fw(\))19 b Fm(2)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4796
Fn(\000)p 770 1312 729 4 v 892 1385 a(\000)32 b Fm(`)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4797
b Fk(var)9 b Fw(\()p Fn(x)p Fw(\))20 b(:)i Fn(T)1540
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4798
1329 y Fw(T)n(yp)r(e)1713 1347 y Fx(1)1901 1284 y Fn(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4799
b Fm(`)21 b Fn(M)30 b Fw(:)21 b Fn(T)2239 1292 y Fx(1)2295
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4800
1284 y Fm(!)g Fn(T)2438 1292 y Fx(2)2549 1284 y Fn(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4801
b Fm(`)21 b Fn(N)30 b Fw(:)22 b Fn(T)2875 1292 y Fx(1)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4802
1901 1312 1009 4 v 2078 1385 a Fn(\000)32 b Fm(`)21 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4803
Fk(app)5 b Fw(\()p Fn(M)t(;)13 b(N)8 b Fw(\))22 b(:)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4804
Fn(T)2698 1393 y Fx(2)2951 1329 y Fw(T)n(yp)r(e)3124
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4805
1347 y Fx(2)1360 1539 y Fn(x)f Fw(#)g Fn(\000)109 b Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4806
Fn(x)9 b Fw(:)g Fn(T)1824 1547 y Fx(1)1857 1539 y Fw(\))g(::)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4807
Fn(\000)31 b Fm(`)22 b Fn(M)29 b Fw(:)22 b Fn(T)2285
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4808
1547 y Fx(2)p 1360 1578 960 4 v 1428 1651 a Fn(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4809
b Fm(`)21 b Fk(lam)5 b Fw(\()p Fn(x:M)j Fw(\))21 b(:)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4810
Fn(T)2018 1659 y Fx(1)2074 1651 y Fm(!)f Fn(T)2217 1659
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4811
y Fx(2)2361 1594 y Fw(T)n(yp)r(e)2534 1613 y Fx(3)3307
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4812
1467 y Fw(\(2\))523 1821 y Fz(where)30 b(\()p Fr(x)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4813
Fz(:)f Fr(T)12 b Fz(\))27 b Fp(2)g Fr(\000)42 b Fz(stands)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4814
b(for)f(list-mem)n(b)r(ership,)h(and)g Fr(x)e Fz(#)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4815
Fr(\000)42 b Fz(for)30 b Fr(x)g Fz(b)r(eing)h(fresh)f(for)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4816
1921 y Fr(\000)12 b Fz(,)31 b(or)e(equiv)-5 b(alen)n(tly)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4817
b Fr(x)g Fz(not)g(o)r(ccuring)f(in)h Fr(\000)12 b Fz(.)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4818
b(De\014ne)i(a)e(con)n(text)g Fr(\000)2686 1891 y Fj(0)2740
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4819
1921 y Fz(to)h(b)r(e)g(w)n(eak)n(er)e(than)523 2020 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4820
Fr(\000)42 b Fz(\(written)31 b Fr(\000)39 b Fp(\022)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4821
b Fr(\000)1187 1990 y Fj(0)1210 2020 y Fz(\),)j(if)h(ev)n(ery)e(name-t)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4822
n(yp)r(e)h(pair)g(in)g Fr(\000)42 b Fz(also)29 b(app)r(ears)g(in)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4823
Fr(\000)3015 1990 y Fj(0)3038 2020 y Fz(.)f(Then)g(w)n(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4824
2120 y(ha)n(v)n(e)523 2271 y Ft(Lemma)f(\(W)-8 b(eak)m(ening\).)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4825
b Fs(If)k Fr(\000)40 b Fp(`)29 b Fr(M)37 b Fz(:)29 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4826
Fr(T)44 b Fs(is)33 b(derivable,)j(and)d Fr(\000)40 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4827
Fp(\022)29 b Fr(\000)2852 2241 y Fj(0)2907 2271 y Fs(with)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4828
b Fr(\000)3154 2241 y Fj(0)3210 2271 y Fs(valid,)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4829
2371 y(then)c Fr(\000)771 2340 y Fj(0)817 2371 y Fp(`)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4830
b Fr(M)32 b Fz(:)23 b Fr(T)41 b Fs(is)30 b(also)h(derivable.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4831
2521 y Fz(The)k(informal)f(pro)r(of)g(of)g(this)h(lemma)f(is)h(straigh)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4832
n(tforw)n(ard,)c(pro)n(vided\(!\))j(one)h(uses)f(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4833
2621 y(v)-5 b(ariable)27 b(con)n(v)n(en)n(tion.)523 2747
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4834
y Fs(Informal)37 b(Pr)l(o)l(of)p Fz(.)f Fs(By)h(rule)f(induction)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4835
(over)g Fr(\000)46 b Fp(`)35 b Fr(M)43 b Fz(:)35 b Fr(T)47
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4836
b Fs(showing)37 b(that)g Fr(\000)3020 2716 y Fj(0)3077
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4837
2747 y Fp(`)e Fr(M)43 b Fz(:)35 b Fr(T)523 2846 y Fs(holds)c(for)g(al)t
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4838
(l)g Fr(\000)1050 2816 y Fj(0)1102 2846 y Fs(with)g Fr(\000)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4839
Fp(\022)23 b Fr(\000)1519 2816 y Fj(0)1571 2846 y Fs(and)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4840
b Fr(\000)1796 2816 y Fj(0)1848 2846 y Fs(b)l(eing)g(valid.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4841
2972 y Ft(Case)e Fz(T)n(yp)r(e)936 2984 y Fy(1)974 2972
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4842
y Fz(:)g Fr(\000)38 b Fp(`)26 b Fr(M)35 b Fz(:)27 b Fr(T)42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4843
b Fs(is)32 b Fr(\000)38 b Fp(`)26 b Fs(var)10 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4844
Fr(x)p Fz(\))27 b(:)g Fr(T)12 b Fs(.)31 b(By)h(assumption)g(we)g(know)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4845
Fr(v)s(al)r(id)p Fz(\()p Fr(\000)3325 2942 y Fj(0)3347
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4846
2972 y Fz(\))p Fs(,)523 3071 y Fz(\()p Fr(x)9 b Fz(:)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4847
Fr(T)j Fz(\))24 b Fp(2)f Fr(\000)41 b Fs(and)31 b Fr(\000)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4848
Fp(\022)23 b Fr(\000)1328 3041 y Fj(0)1351 3071 y Fs(.)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4849
b(Ther)l(efor)l(e)i(we)e(c)l(an)f(use)h Fz(T)n(yp)r(e)2391
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4850
3083 y Fy(1)2458 3071 y Fs(to)f(derive)i Fr(\000)2867
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4851
3041 y Fj(0)2913 3071 y Fp(`)23 b Fs(var)10 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4852
Fr(x)p Fz(\))24 b(:)f Fr(T)12 b Fs(.)523 3197 y Ft(Case)41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4853
b Fz(T)n(yp)r(e)948 3209 y Fy(2)985 3197 y Fz(:)h Fr(\000)58
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4854
b Fp(`)45 b Fr(M)55 b Fz(:)46 b Fr(T)54 b Fs(is)43 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4855
Fr(\000)57 b Fp(`)46 b Fs(app)7 b Fz(\()p Fr(M)2116 3209
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4856
y Fy(1)2153 3197 y Fr(;)14 b(M)2271 3209 y Fy(2)2307
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4857
3197 y Fz(\))47 b(:)f Fr(T)12 b Fs(.)42 b(Case)h(fol)t(lows)i(fr)l(om)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4858
(the)523 3297 y(induction)30 b(hyp)l(otheses)i(and)e(rule)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4859
Fz(T)n(yp)r(e)1816 3309 y Fy(2)1854 3297 y Fs(.)523 3422
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4860
y Ft(Case)38 b Fz(T)n(yp)r(e)945 3434 y Fy(3)983 3422
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4861
y Fz(:)g Fr(\000)53 b Fp(`)41 b Fr(M)50 b Fz(:)42 b Fr(T)51
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4862
b Fs(is)40 b Fr(\000)53 b Fp(`)41 b Fs(lam)7 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4863
Fr(x:M)2152 3434 y Fy(1)2189 3422 y Fz(\))42 b(:)f Fr(T)2376
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4864
3434 y Fy(1)2455 3422 y Fp(!)g Fr(T)2628 3434 y Fy(2)2665
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4865
3422 y Fs(.)f(Using)g(the)g(variable)523 3522 y(c)l(onvention)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4866
b(we)g(assume)g(that)f Fr(x)f Fz(#)f Fr(\000)1734 3492
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4867
y Fj(0)1757 3522 y Fs(.)j(Then)g(we)g(know)g(that)g Fz(\(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4868
Fr(x)9 b Fz(:)g Fr(T)2714 3534 y Fy(1)2752 3522 y Fz(\))g(::)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4869
Fr(\000)2911 3492 y Fj(0)2935 3522 y Fz(\))26 b Fs(is)g(valid)h(and)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4870
3621 y(henc)l(e)f(that)g Fz(\(\()p Fr(x)9 b Fz(:)g Fr(T)1115
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4871
3633 y Fy(1)1154 3621 y Fz(\))g(::)g Fr(\000)1313 3591
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4872
y Fj(0)1336 3621 y Fz(\))24 b Fp(`)f Fr(M)1547 3633 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4873
Fy(1)1606 3621 y Fz(:)h Fr(T)1702 3633 y Fy(2)1764 3621
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4874
y Fs(holds.)k(By)f(app)l(e)l(aling)h(to)e(the)g(variable)i(c)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4875
(onvention)523 3721 y(again,)j(we)f(have)h(that)f Fr(\000)1320
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4876
3691 y Fj(0)1366 3721 y Fp(`)23 b Fs(lam)7 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4877
Fr(x:M)1761 3733 y Fy(1)1798 3721 y Fz(\))24 b(:)f Fr(T)1949
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4878
3733 y Fy(1)2009 3721 y Fp(!)g Fr(T)2164 3733 y Fy(2)2230
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4879
3721 y Fs(holds)31 b(using)f(rule)g Fz(T)n(yp)r(e)3017
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4880
3733 y Fy(3)3350 3721 y Fp(u)-55 b(t)523 3897 y Fz(Ho)n(w)n(ev)n(er,)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4881
b(in)i(order)e(to)i(mak)n(e)e(this)i(informal)f(pro)r(of)h(w)n(ork)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4882
(with)i(the)g(induction)g(principle)523 3997 y(that)j(comes)f(with)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4883
(the)g(rules)f(in)h(\(2\),)g(namely)605 4180 y Fp(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4884
Fr(\000)d(x)14 b(T)7 b(:)45 b Fs(valid)11 b Fz(\()p Fr(\000)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4885
Fz(\))18 b Fp(^)h Fz(\()p Fr(x)9 b Fz(:)g Fr(T)j Fz(\))24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4886
b Fp(2)f Fr(\000)35 b Fp(\))23 b Fr(P)35 b(\000)g Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4887
Fs(var)9 b Fz(\()p Fr(x)p Fz(\)\))25 b Fr(T)605 4303
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4888
y Fp(8)p Fr(\000)g(M)d(N)h(T)970 4315 y Fy(1)1020 4303
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4889
y Fr(T)1069 4315 y Fy(2)1106 4303 y Fr(:)g(P)35 b(\000)g(M)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4890
Fz(\()p Fr(T)1519 4315 y Fy(1)1579 4303 y Fp(!)23 b Fr(T)1734
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4891
4315 y Fy(2)1771 4303 y Fz(\))42 b Fp(^)g Fr(P)35 b(\000)f(N)e(T)2263
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4892
4315 y Fy(1)2346 4303 y Fp(\))23 b Fr(P)35 b(\000)g Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4893
Fs(app)7 b Fz(\()p Fr(M)t(;)14 b(N)9 b Fz(\)\))23 b Fr(T)3157
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4894
4315 y Fy(2)605 4426 y Fp(8)p Fr(x)14 b(\000)25 b(M)d(T)941
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4895
4438 y Fy(1)992 4426 y Fr(T)1041 4438 y Fy(2)1078 4426
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4896
y Fr(:)h(x)g Fz(#)g Fr(\000)31 b Fp(^)18 b Fr(P)35 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4897
Fz(\(\()p Fr(x)9 b Fz(:)g Fr(T)1730 4438 y Fy(1)1769
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4898
4426 y Fz(\))g(::)g Fr(\000)j Fz(\))23 b Fr(M)32 b(T)2145
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4899
4438 y Fy(2)2228 4426 y Fp(\))23 b Fr(P)35 b(\000)g Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4900
Fs(lam)7 b Fz(\()p Fr(x:M)i Fz(\)\))24 b(\()p Fr(T)3039
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4901
4438 y Fy(1)3099 4426 y Fp(!)f Fr(T)3254 4438 y Fy(2)3291
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4902
4426 y Fz(\))p 593 4476 2742 4 v 1514 4550 a Fr(\000)35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4903
b Fp(`)23 b Fr(M)31 b Fz(:)23 b Fr(T)57 b Fp(\))47 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4904
Fr(P)35 b(\000)f(M)e(T)3299 4650 y Fz(\(3\))523 4742
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4905
y(w)n(e)i(need)g(in)g(case)f(of)h(rule)f(T)n(yp)r(e)1597
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4906
4754 y Fy(3)1669 4742 y Fz(to)g(b)r(e)i(able)e(to)h(rename)f(the)i(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4907
(ound)f(v)-5 b(ariable)33 b(to)h(b)r(e)523 4833 y(suitably)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4908
b(fresh)g(for)g Fr(\000)1209 4803 y Fj(0)1232 4833 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4909
Fz(;)g(b)n(y)g(the)h(induction)g(w)n(e)f(only)f(kno)n(w)h(that)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4910
Fr(x)h Fz(is)f(fresh)h(for)e(the)i(smaller)523 4924 y(con)n(text)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4911
Fr(\000)12 b Fz(.)22 b(T)-7 b(o)22 b(b)r(e)h(able)f(to)g(do)g(this)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4912
(renaming)e(dep)r(ends)i(on)f(t)n(w)n(o)g(conditions:)g(\014rst,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4913
(there)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4914
%%Page: 4 4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4915
TeXDict begin 4 3 bop Black 523 232 a Fw(4)237 b(Christian)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4916
b(Urban,)e(Stefan)h(Berghofer,)i(and)d(Mic)n(hael)i(Norrish)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4917
Black 523 448 a Fz(m)n(ust)d(exist)h(a)f(fresh)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4918
b(ariable)23 b(whic)n(h)h(w)n(e)g(can)g(c)n(ho)r(ose.)f(In)i(our)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4919
(example)h(this)h(means)f(that)523 540 y(the)k(con)n(text)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4920
Fr(\000)1025 510 y Fj(0)1076 540 y Fz(m)n(ust)g(not)g(con)n(tain)g(all)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4921
f(p)r(ossible)h(free)g(v)-5 b(ariables.)27 b(Second,)h(the)g(relation)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4922
523 631 y Fr(\000)42 b Fp(`)30 b Fr(M)39 b Fz(:)31 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4923
Fr(T)43 b Fz(m)n(ust)32 b(b)r(e)h(in)n(v)-5 b(arian)n(t)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4924
b(under)g(suitable)h(renamings.)f(This)h(is)g(b)r(ecause)g(when)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4925
722 y(w)n(e)j(c)n(hange)g(the)h(goal)f(from)g Fr(\000)1538
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4926
692 y Fj(0)1598 722 y Fp(`)h Fs(lam)7 b Fz(\()p Fr(x:M)2006
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4927
734 y Fy(1)2044 722 y Fz(\))37 b(:)g Fr(T)2222 734 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4928
Fy(1)2295 722 y Fp(!)g Fr(T)2464 734 y Fy(2)2537 722
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4929
y Fz(to)f Fr(\000)2710 692 y Fj(0)2769 722 y Fp(`)h Fs(lam)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4930
b Fz(\()p Fr(z)t(:M)3174 734 y Fy(1)3210 722 y Fz([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4931
Fr(x)37 b Fz(:=)523 814 y Fr(z)t Fz(]\))g(:)h Fr(T)768
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4932
826 y Fy(1)842 814 y Fp(!)g Fr(T)1012 826 y Fy(2)1049
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4933
814 y Fz(,)e(w)n(e)g(m)n(ust)h(b)r(e)g(able)f(to)g(infer)g(from)g(\(\()
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4934
p Fr(x)25 b Fz(:)f Fr(T)2507 826 y Fy(1)2544 814 y Fz(\))g(::)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4935
Fr(\000)2733 783 y Fj(0)2756 814 y Fz(\))38 b Fp(`)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4936
Fr(M)2995 826 y Fy(1)3070 814 y Fz(:)h Fr(T)3180 826
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4937
y Fy(2)3253 814 y Fz(that)523 905 y(\(\()p Fr(z)23 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4938
Fz(:)18 b Fr(T)739 917 y Fy(1)776 905 y Fz(\))h(::)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4939
Fr(\000)955 875 y Fj(0)978 905 y Fz(\))32 b Fp(`)h Fr(M)1207
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4940
917 y Fy(1)1243 905 y Fz([)p Fr(x)g Fz(:=)g Fr(z)t Fz(])e(:)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4941
Fr(T)1669 917 y Fy(2)1739 905 y Fz(holds.)g(This)g(in)n(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4942
b(ariance)32 b(under)h(renamings)f(do)r(es,)523 996 y(ho)n(w)n(ev)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4943
(er,)21 b Fs(not)31 b Fz(hold)24 b(in)f(general,)f(not)h(ev)n(en)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4944
(under)h(renamings)e(with)h(fresh)h(v)-5 b(ariables.)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4945
b(F)-7 b(or)523 1088 y(example)27 b(if)h(w)n(e)g(assume)e(that)i(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4946
b(ariables)27 b(are)f(linearly)h(ordered,)f(then)i(the)g(relation)1626
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4947
1232 y Fn(v)c Fw(=)d Fk(min)5 b Fm(f)p Fn(v)1978 1240
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4948
y Fx(0)2014 1232 y Fn(;)13 b(:)g(:)g(:)g(;)g(v)2221 1240
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4949
y Fi(n)2264 1232 y Fm(g)p 1626 1270 677 4 v 1697 1343
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4950
a Fw(\()p Fm(f)p Fn(v)1802 1351 y Fx(0)1838 1343 y Fn(;)g(:)g(:)g(:)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4951
(;)g(v)2045 1351 y Fi(n)2088 1343 y Fm(g)p Fn(;)h(v)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4952
Fw(\))523 1506 y Fz(that)24 b(asso)r(ciates)e(\014nite)i(subsets)f(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4953
(these)h(v)-5 b(ariables)22 b(to)h(the)h(smallest)f(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4954
b(ariable)22 b(o)r(ccurring)523 1606 y(in)k(it,)h(is)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4955
Fs(not)34 b Fz(in)n(v)-5 b(arian)n(t)25 b(\(apply)h(the)g(renaming)f([)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4956
p Fr(v)h Fz(:=)d Fr(v)2308 1575 y Fj(0)2332 1606 y Fz(])j(where)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4957
Fr(v)2662 1575 y Fj(0)2712 1606 y Fz(is)g(a)h(v)-5 b(ariable)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4958
b(that)h(is)523 1705 y(bigger)20 b(than)h(ev)n(ery)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4959
b(ariable)20 b(in)h Fp(f)p Fr(v)1644 1717 y Fy(0)1681
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4960
1705 y Fr(;)14 b(:)g(:)g(:)g(;)g(v)1906 1717 y Fq(n)1951
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4961
1705 y Fp(g)p Fz(\).)22 b(Other)e(examples)h(are)f(rules)h(that)h(in)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4962
(v)n(olv)n(e)523 1805 y(a)34 b(substitution)g(for)g(concrete)f(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4963
b(ariables)33 b(or)g(a)h(substitution)g(with)h(concrete)e(terms.)h(In)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4964
523 1904 y(order)22 b(to)h(a)n(v)n(oid)e(suc)n(h)i(pathological)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4965
(cases,)h(w)n(e)h(require)f(that)h(the)h(relation)e(for)g(whic)n(h)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4966
(one)523 2004 y(w)n(an)n(ts)36 b(to)h(emplo)n(y)f(the)i(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4967
b(ariable)36 b(con)n(v)n(en)n(tion)f(m)n(ust)i(b)r(e)h(in)n(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4968
b(arian)n(t)35 b(under)i(renamings;)523 2104 y(from)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4969
b(the)h(induction)g(w)n(e)g(require)e(that)i(the)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4970
b(ariable)27 b(con)n(v)n(en)n(tion)h(can)g(only)g(b)r(e)h(applied)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4971
2203 y(in)f(con)n(texts)f(where)g(there)g(are)g(only)g(\014nitely)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4972
(man)n(y)f(free)h(names.)648 2295 y(Ho)n(w)n(ev)n(er,)g(these)j(t)n(w)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4973
(o)f(requiremen)n(ts)f(are)h Fs(not)38 b Fz(y)n(et)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4974
b(su\016cien)n(t,)h(and)g(w)n(e)f(need)h(to)f(im-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4975
2386 y(p)r(ose)f(a)g(second)g(condition)h(that)g(inductiv)n(e)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4976
(de\014nitions)h(ha)n(v)n(e)e(to)i(satisfy)-7 b(.)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4977
b(Consider)g(the)523 2477 y(function)f(that)g(tak)n(es)f(a)g(list)h(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4978
f(v)-5 b(ariables)27 b(and)g(binds)h(them)g(in)g Fr(\025)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4979
Fz(-abstractions,)e(that)i(is)1034 2657 y Fk(bind)i Fn(t)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4980
b Fw([)13 b(])1352 2614 y Fy(def)1365 2657 y Fw(=)56
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4981
b Fn(t)154 b Fk(bind)29 b Fn(t)21 b Fw(\()p Fn(x)9 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4982
Fw(::)g Fk(xs)d Fw(\))2160 2614 y Fy(def)2174 2657 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4983
Fw(=)56 b Fk(lam)5 b Fw(\()p Fn(x:)p Fw(\()p Fk(bind)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4984
b Fn(t)21 b Fk(xs)7 b Fw(\)\))523 2820 y Fz(F)-7 b(urther)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4985
b(consider)f(the)h(relation)f Fr(,)-14 b Fp(!)p Fz(,)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4986
b(whic)n(h)f(\\un)n(binds")f(the)h(outermost)g(abstractions)e(of)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4987
2919 y(a)27 b Fr(\025)p Fz(-term)h(and)f(is)h(de\014ned)g(b)n(y:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4988
641 3053 709 4 v 641 3132 a Fs(var)10 b Fz(\()p Fr(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4989
Fz(\))24 b Fr(,)-14 b Fp(!)23 b Fz([)14 b(])p Fr(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4990
Fs(var)c Fz(\()p Fr(x)p Fz(\))1391 3076 y(Un)n(bind)1659
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4991
3088 y Fy(1)p 1862 3053 973 4 v 1862 3132 a Fs(app)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4992
Fz(\()p Fr(t)2057 3144 y Fy(1)2094 3132 y Fr(;)14 b(t)2161
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4993
3144 y Fy(2)2198 3132 y Fz(\))24 b Fr(,)-14 b Fp(!)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4994
b Fz([)14 b(])p Fr(;)g Fs(app)6 b Fz(\()p Fr(t)2660 3144
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4995
y Fy(1)2698 3132 y Fr(;)14 b(t)2765 3144 y Fy(2)2802
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4996
3132 y Fz(\))2876 3076 y(Un)n(bind)3143 3088 y Fy(2)1569
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4997
3248 y Fr(t)23 b(,)-14 b Fp(!)23 b Fs(xs)7 b Fr(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4998
b(t)1884 3218 y Fj(0)p 1376 3284 723 4 v 1376 3363 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4999
Fs(lam)7 b Fz(\()p Fr(x:t)p Fz(\))24 b Fr(,)-14 b Fp(!)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5000
b Fr(x)9 b Fz(::)g Fs(xs)e Fr(;)14 b(t)2076 3333 y Fj(0)2141
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5001
3306 y Fz(Un)n(bind)2408 3319 y Fy(3)3299 3226 y Fz(\(4\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5002
3533 y(Of)35 b(course,)f(this)h(relation)f(cannot)g(b)r(e)i(expressed)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5003
(as)g(a)g(function)i(b)r(ecause)e(the)i(b)r(ound)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5004
3624 y(v)-5 b(ariables)23 b(do)g(not)h(ha)n(v)n(e)f(\\particular")e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5005
(names.)j(Nonetheless)f(it)i(is)f(w)n(ell-de\014ned,)f(and)h(not)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5006
3716 y(trivial.)j(F)-7 b(or)27 b(example,)g(w)n(e)h(ha)n(v)n(e)647
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5007
3867 y Fk(lam)6 b Fw(\()p Fn(x:)p Fk(lam)f Fw(\()p Fn(y)s(:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5008
Fk(app)g Fw(\()p Fk(var)j Fw(\()p Fn(x)p Fw(\))p Fn(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5009
b Fk(app)5 b Fw(\()p Fk(var)k Fw(\()p Fn(y)s Fw(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5010
Fn(;)j Fk(var)d Fw(\()p Fn(z)s Fw(\)\)\)\)\))1734 3959
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5011
y Fn(,)-13 b Fm(!)21 b Fw([)p Fn(x;)13 b(y)s Fw(])p Fn(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5012
Fk(app)6 b Fw(\()p Fk(var)i Fw(\()p Fn(x)p Fw(\))p Fn(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5013
b Fk(app)5 b Fw(\()p Fk(var)k Fw(\()p Fn(y)s Fw(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5014
Fn(;)j Fk(var)d Fw(\()p Fn(z)s Fw(\)\)\))42 b(and)647
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5015
4074 y Fk(lam)6 b Fw(\()p Fn(x:)p Fk(lam)f Fw(\()p Fn(y)s(:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5016
Fk(app)g Fw(\()p Fk(var)j Fw(\()p Fn(x)p Fw(\))p Fn(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5017
b Fk(app)5 b Fw(\()p Fk(var)k Fw(\()p Fn(y)s Fw(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5018
Fn(;)j Fk(var)d Fw(\()p Fn(z)s Fw(\)\)\)\)\))1734 4165
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5019
y Fn(,)-13 b Fm(!)21 b Fw([)p Fn(y)s(;)13 b(x)p Fw(])p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5020
Fn(;)g Fk(app)6 b Fw(\()p Fk(var)i Fw(\()p Fn(y)s Fw(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5021
Fn(;)13 b Fk(app)5 b Fw(\()p Fk(var)k Fw(\()p Fn(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5022
Fw(\))p Fn(;)j Fk(var)d Fw(\()p Fn(z)s Fw(\)\)\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5023
4327 y Fz(but)28 b(w)n(e)f(also)g(ha)n(v)n(e)f Fp(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5024
Fr(t)1232 4296 y Fj(0)1255 4327 y Fr(:)d Fs(lam)7 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5025
Fr(x:)p Fs(lam)h Fz(\()p Fr(y)s(:)p Fs(app)e Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5026
Fr(x;)14 b Fs(app)7 b Fz(\()p Fs(var)j Fz(\()p Fr(y)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5027
Fz(\))p Fr(;)k Fs(var)c Fz(\()p Fr(z)t Fz(\)\)\)\)\))24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5028
b Fp(6)p Fr(,)-14 b Fp(!)23 b Fz([)p Fr(x;)14 b(z)t Fz(])p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5029
Fr(;)g(t)3201 4296 y Fj(0)3224 4327 y Fz(.)648 4426 y(F)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5030
b(urther,)31 b(one)g(can)g(also)f(easily)g(establish)h(\(b)n(y)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5031
(induction)f(on)g(the)h(term)f Fr(t)p Fz(\))h(that)g(for)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5032
4526 y(ev)n(ery)f Fr(t)i Fz(there)g(exists)f(a)g Fr(t)1366
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5033
4496 y Fj(0)1422 4526 y Fz(and)h(a)f(list)h Fs(xs)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5034
b Fz(of)32 b(distinct)i(v)-5 b(ariables)31 b(suc)n(h)h(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5035
Fr(t)f(,)-14 b Fp(!)31 b Fs(xs)7 b Fr(;)14 b(t)3382 4496
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5036
y Fj(0)523 4625 y Fz(holds,)29 b(demonstrating)g(that)h(the)g(relation)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5037
f(is)h(\\total")e(if)i(the)h(last)e(t)n(w)n(o)g(parameters)f(are)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5038
4725 y(view)n(ed)f(as)g(results.)648 4825 y(If)33 b(one)f(wished)h(to)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5039
(do)h(rule)f(inductions)h(o)n(v)n(er)e(the)i(de\014nition)g(of)g(this)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5040
(relation,)e(one)523 4924 y(migh)n(t)23 b(imagine)f(that)i(the)f(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5041
b(ariable)22 b(con)n(v)n(en)n(tion)f(allo)n(w)n(ed)h(us)h(to)g(assume)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5042
(that)h(the)h(b)r(ound)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5043
%%Page: 5 5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5044
TeXDict begin 5 4 bop Black 1347 232 a Fw(Barendregt's)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5045
b(V)-6 b(ariable)26 b(Con)n(v)n(en)n(tion)f(in)h(Rule)f(Inductions)237
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5046
b(5)p Black 523 448 a Fz(name)33 b Fr(x)h Fz(w)n(as)f(distinct)h(from)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5047
(the)h(free)f(v)-5 b(ariables)33 b(of)g(the)h(conclusion)f(of)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5048
(rule,)f(and)523 548 y(in)j(particular)e(that)i Fr(x)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5049
Fz(could)e(not)h(app)r(ear)f(in)h(the)g(list)g Fs(xs)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5050
b Fz(.)36 b(Ho)n(w)n(ev)n(er,)d(this)j(use)g(of)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5051
648 y(v)-5 b(ariable)27 b(con)n(v)n(en)n(tion)f(quic)n(kly)h(leads)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5052
(to)g(the)h Fs(faulty)36 b Fz(lemma:)523 792 y Ft(Lemma)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5053
b(\(F)-8 b(ault)m(y\).)78 b Fs(If)28 b Fr(t)c(,)-14 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5054
Fp(!)23 b Fz(\()p Fr(x)9 b Fz(::)g Fs(xs)e Fz(\))p Fr(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5055
b(t)1873 762 y Fj(0)1925 792 y Fs(and)29 b Fr(x)23 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5056
Fp(2)g Fr(F)12 b(V)19 b Fz(\()p Fr(t)2427 762 y Fj(0)2451
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5057
792 y Fz(\))28 b Fs(then)g Fr(x)c Fp(2)f Fr(F)12 b(V)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5058
b Fz(\()p Fs(bind)33 b Fr(t)3222 762 y Fj(0)3268 792
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5059
y Fs(xs)6 b Fz(\))p Fs(.)523 937 y Fz(The)26 b(\\pro)r(of)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5060
b(")25 b(is)h(b)n(y)g(an)g(induction)h(o)n(v)n(er)d(the)i(rules)g(giv)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5061
(en)f(in)i(\(4\))f(and)g(assumes)f(that)i(the)523 1036
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5062
y(binder)33 b Fr(x)g Fz(in)g(the)g(third)g(rule)g(is)f(fresh)h(with)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5063
(resp)r(ect)g(to)f Fs(xs)7 b Fz(.)32 b(This)h(lemma)g(is)g(of)f(course)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5064
523 1136 y(false)h(as)g(witnessed)h(b)n(y)f(the)h(term)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5065
Fs(lam)7 b Fz(\()p Fr(x:)p Fs(lam)h Fz(\()p Fr(x:)p Fs(var)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5066
Fz(\()p Fr(x)p Fz(\)\)\).)36 b(Therefore,)c(including)i(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5067
1236 y(v)-5 b(ariable)29 b(con)n(v)n(en)n(tion)f(in)h(the)h(induction)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5068
(principle)g(that)f(comes)g(with)h(the)g(rules)f(in)h(\(4\),)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5069
1335 y(w)n(ould)25 b(pro)r(duce)h(an)f(inconsistency)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5070
b(.)26 b(T)-7 b(o)25 b(prev)n(en)n(t)g(this)h(problem)f(w)n(e)h(in)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5071
(tro)r(duce)f(a)h(second)523 1435 y(condition)37 b(for)f(rules,)h(whic)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5072
n(h)g(requires)e(that)j(all)f(v)-5 b(ariables)35 b(o)r(ccurring)h(as)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5073
(a)h(binder)g(in)523 1535 y(a)g(rule)f(m)n(ust)h(b)r(e)g(fresh)g(\(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5074
(notion)f(whic)n(h)h(w)n(e)g(shall)f(mak)n(e)g(precise)g(later)g(on\))h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5075
(for)g(the)523 1634 y(conclusion)d(of)i(this)f(rule,)g(and)h(if)f(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5076
(rule)g(has)g(sev)n(eral)f(suc)n(h)h(v)-5 b(ariables,)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5077
b(they)h(m)n(ust)h(b)r(e)523 1734 y(m)n(utually)28 b(distinct.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5078
1878 y Ft(Our)44 b(Con)m(tribution:)37 b Fz(W)-7 b(e)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5079
b(in)n(tro)r(duce)e(t)n(w)n(o)h(conditions)f(inductiv)n(e)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5080
(de\014nitions)f(m)n(ust)523 1978 y(satisfy)28 b(in)h(order)e(to)h(mak)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5081
n(e)g(sure)g(they)g(are)g(compatible)g(with)h(the)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5082
b(ariable)27 b(con)n(v)n(en)n(tion.)523 2078 y(W)-7 b(e)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5083
b(will)h(build)f(a)g(v)n(ersion)f(of)h(this)g(con)n(v)n(en)n(tion)f(in)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5084
n(to)g(the)i(induction)f(principles)g(that)g(come)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5085
2177 y(with)31 b(the)g(inductiv)n(e)g(de\014nitions.)g(Moreo)n(v)n(er,)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5086
d(it)j(will)g(b)r(e)g(sho)n(wn)f(ho)n(w)g(these)g(new)h(\(\\v)n(c-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5087
2277 y(compatible"\))g(induction)g(principles)g(can)f(b)r(e)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5088
(automatically)e(deriv)n(ed)g(in)h(the)g(nominal)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5089
2377 y(datat)n(yp)r(e)36 b(pac)n(k)-5 b(age)36 b([11,)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5090
b(9].)37 b(The)g(presen)n(ted)f(results)g(ha)n(v)n(e)f(already)h(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5091
(een)h(extensiv)n(ely)523 2476 y(used)j(in)h(formalisations:)d(for)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5092
(example)g(in)g(our)g(formalisations)e(of)i(the)h(CR)f(and)h(SN)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5093
2576 y(prop)r(erties)f(in)h(the)g Fr(\025)p Fz(-calculus,)f(in)h(a)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5094
(formalisation)f(b)n(y)i(Bengtson)e(and)i(P)n(arro)n(w)d(for)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5095
2676 y(sev)n(eral)f(pro)r(ofs)g(in)i(the)g(pi-calculus)e([3],)h(in)h(a)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5096
f(formalisation)f(of)h(Crary's)f(c)n(hapter)g(on)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5097
2775 y(logical)d(relation)h([4],)h(and)f(in)h(v)-5 b(arious)35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5098
b(formalised)f(pro)r(ofs)h(on)h(structural)f(op)r(erational)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5099
2875 y(seman)n(tics.)523 3131 y Fu(2)112 b(Nominal)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5100
b(Logic)523 3312 y Fz(Before)d(pro)r(ceeding,)g(w)n(e)g(brie\015y)h(in)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5101
n(tro)r(duce)f(some)g(imp)r(ortan)n(t)h(notions)f(from)g(nominal)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5102
3404 y(logic)25 b([8,)13 b(11].)25 b(In)h(particular,)e(w)n(e)h(will)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5103
(build)g(on)g(the)g(three)f(cen)n(tral)g(notions)g(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5104
Fs(p)l(ermuta-)523 3495 y(tions)p Fz(,)f Fs(supp)l(ort)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5105
b Fz(and)23 b Fs(e)l(quivarianc)l(e)p Fz(.)i(P)n(erm)n(utations)d(are)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5106
(\014nite)i(bijectiv)n(e)g(mappings)e(from)523 3586 y(atoms)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5107
b(to)g(atoms,)g(where)g(atoms)g(are)g(dra)n(wn)f(from)h(a)g(coun)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5108
(tably)g(in\014nite)h(set)g(denoted)523 3677 y(b)n(y)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5109
Fh(A)17 b Fz(.)40 b(W)-7 b(e)34 b(represen)n(t)f(p)r(erm)n(utations)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5110
(as)h(\014nite)g(lists)g(whose)f(elemen)n(ts)h(are)f(sw)n(appings)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5111
3769 y(\(i.e.,)k(pairs)f(of)g(atoms\).)h(W)-7 b(e)37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5112
b(write)f(suc)n(h)g(p)r(erm)n(utations)g(as)g(\()p Fr(a)2620
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5113
3781 y Fy(1)2671 3769 y Fr(b)2707 3781 y Fy(1)2744 3769
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5114
y Fz(\)\()p Fr(a)2852 3781 y Fy(2)2904 3769 y Fr(b)2940
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5115
3781 y Fy(2)2977 3769 y Fz(\))14 b Fp(\001)g(\001)g(\001)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5116
Fz(\()p Fr(a)3210 3781 y Fq(n)3269 3769 y Fr(b)3305 3781
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5117
y Fq(n)3350 3769 y Fz(\);)523 3860 y(the)33 b(empt)n(y)g(list)g([)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5118
b(])33 b(stands)f(for)h(the)g(iden)n(tit)n(y)g(p)r(erm)n(utation.)g(A)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5119
(p)r(erm)n(utation)f Fr(\031)k Fs(acting)523 3951 y Fz(on)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5120
b(an)h(atom)f Fr(a)g Fz(is)h(de\014ned)g(as:)1111 4176
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5121
y Fw([)13 b(])1166 4185 y Fg(\001)1205 4176 y Fn(a)1269
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5122
4134 y Fy(def)1282 4176 y Fw(=)37 b Fn(a)176 b Fw(\(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5123
Fn(a)1697 4184 y Fx(1)1744 4176 y Fn(a)1785 4184 y Fx(2)1819
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5124
4176 y Fw(\))9 b(::)g Fn(\031)s Fw(\))1986 4185 y Fg(\001)2023
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5125
4176 y Fn(a)2087 4134 y Fy(def)2101 4176 y Fw(=)2197
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5126
4023 y Ff(8)2197 4090 y(<)2197 4225 y(:)2277 4085 y Fn(a)2318
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5127
4093 y Fx(2)2426 4085 y Fw(if)22 b Fn(\031)2539 4094
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5128
y Fg(\001)2577 4085 y Fn(a)f Fw(=)g Fn(a)2761 4093 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5129
Fx(1)2277 4176 y Fn(a)2318 4184 y Fx(1)2426 4176 y Fw(if)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5130
Fn(\031)2539 4185 y Fg(\001)2577 4176 y Fn(a)f Fw(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5131
Fn(a)2761 4184 y Fx(2)2277 4267 y Fn(\031)2324 4276 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5132
Fg(\001)2362 4267 y Fn(a)i Fw(otherwise)523 4426 y Fz(where)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5133
b(\()p Fr(a)14 b(b)p Fz(\))21 b(::)f Fr(\031)38 b Fz(is)c(the)h(comp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5134
(osition)f(of)h(a)f(p)r(erm)n(utation)g(follo)n(w)n(ed)f(b)n(y)h(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5135
(sw)n(apping)523 4526 y(\()p Fr(a)14 b(b)p Fz(\).)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5136
b(The)h(comp)r(osition)e(of)h Fr(\031)k Fz(follo)n(w)n(ed)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5137
b(b)n(y)h(another)f(p)r(erm)n(utation)h Fr(\031)2801
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5138
4496 y Fj(0)2852 4526 y Fz(is)g(giv)n(en)f(b)n(y)h(list-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5139
4625 y(concatenation,)c(written)h(as)f Fr(\031)1508 4595
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5140
y Fj(0)1532 4625 y Fz(@)p Fr(\031)s Fz(,)g(and)h(the)g(in)n(v)n(erse)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5141
(of)g(a)h(p)r(erm)n(utation)f(is)h(giv)n(en)f(b)n(y)h(list)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5142
4725 y(rev)n(ersal,)32 b(written)j(as)e Fr(\031)1314
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5143
4695 y Fj(\000)p Fy(1)1404 4725 y Fz(.)h(Our)g(represen)n(tation)e(of)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5144
(p)r(erm)n(utations)g(as)g(lists)g(do)r(es)g(not)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5145
4825 y(giv)n(e)23 b(unique)i(represen)n(tativ)n(es:)d(for)h(example,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5146
(the)h(p)r(erm)n(utation)e(\()p Fr(a)14 b(a)p Fz(\))25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5147
b(is)f(\\equal")f(to)h(the)523 4924 y(iden)n(tit)n(y)k(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5148
(utation.)f(W)-7 b(e)28 b(equate)f(p)r(erm)n(utations)g(with)h(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5149
(relation)e Fp(\030)p Fz(:)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5150
%%Page: 6 6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5151
TeXDict begin 6 5 bop Black 523 232 a Fw(6)237 b(Christian)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5152
b(Urban,)e(Stefan)h(Berghofer,)i(and)d(Mic)n(hael)i(Norrish)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5153
Black Black 523 448 a Ft(De\014nition)k(1)p Black 41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5154
w(\(P)m(erm)m(utation)26 b(Equalit)m(y\).)h Fs(Two)f(p)l(ermutations)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5155
(ar)l(e)32 b Fz(equal)p Fs(,)25 b(written)523 548 y Fr(\031)570
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5156
560 y Fy(1)631 548 y Fp(\030)d Fr(\031)765 560 y Fy(2)803
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5157
548 y Fs(,)30 b(pr)l(ovide)l(d)i Fr(\031)1233 560 y Fy(1)1270
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5158
557 y Fg(\001)1309 548 y Fr(a)23 b Fz(=)f Fr(\031)1510
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5159
560 y Fy(2)1548 557 y Fg(\001)1586 548 y Fr(a)p Fs(,)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5160
b(for)h(al)t(l)f Fr(a)23 b Fp(2)h Fh(A)17 b Fs(.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5161
701 y Fz(The)28 b(p)r(erm)n(utation)f(action)g(on)g(atoms)g(can)g(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5162
(e)h(lifted)h(to)e(other)g(t)n(yp)r(es.)p Black 523 855
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5163
a Ft(De\014nition)k(2)p Black 41 w(\(The)d(Action)g(of)g(a)g(P)m(erm)m
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5164
(utation\).)f Fs(A)f(p)l(ermutation)h(action)g Fr(\031)3237
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5165
864 y Fg(\001)3276 855 y Fz(\()p Fp(\000)p Fz(\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5166
955 y Fs(lifts)e(to)g(a)g(typ)l(e)g Fr(T)36 b Fs(pr)l(ovide)l(d)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5167
b(it)d(the)h(fol)t(lowing)i(thr)l(e)l(e)e(pr)l(op)l(erties)h(hold)g(on)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5168
f(al)t(l)h(values)f Fr(x)e Fp(2)h Fr(T)p Black Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5169
1434 1097 a Fw(\()p Fn(i)p Fw(\))71 b([)13 b(])1646 1106
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5170
y Fg(\001)1685 1097 y Fn(x)21 b Fw(=)g Fn(x)1408 1212
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5171
y Fw(\()p Fn(ii)p Fw(\))71 b(\()p Fn(\031)1665 1220 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5172
Fx(1)1700 1212 y Fw(@)p Fn(\031)1804 1220 y Fx(2)1838
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5173
1212 y Fw(\))1868 1221 y Fg(\001)1906 1212 y Fn(x)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5174
b Fw(=)g Fn(\031)2096 1220 y Fx(1)2130 1221 y Fg(\001)2169
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5175
1212 y Fw(\()p Fn(\031)2243 1220 y Fx(2)2277 1221 y Fg(\001)2315
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5176
1212 y Fn(x)p Fw(\))1382 1327 y(\()p Fn(iii)p Fw(\))71
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5177
b Fk(if)27 b Fn(\031)1710 1335 y Fx(1)1766 1327 y Fm(\030)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5178
b Fn(\031)1891 1335 y Fx(2)1953 1327 y Fk(then)28 b Fn(\031)2167
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5179
1335 y Fx(1)2202 1336 y Fg(\001)2240 1327 y Fn(x)21 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5180
Fw(=)g Fn(\031)2430 1335 y Fx(2)2464 1336 y Fg(\001)2503
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5181
1327 y Fn(x)523 1474 y Fz(F)-7 b(or)27 b(example,)g(lists)h(and)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5182
(tuples)h(can)f(b)r(e)h(giv)n(en)f(the)h(follo)n(wing)f(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5183
(utation)g(action:)1218 1656 y Fw(lists:)479 b Fn(\031)1897
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5184
1665 y Fg(\001)1935 1656 y Fw([)13 b(])2038 1613 y Fy(def)2051
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5185
1656 y Fw(=)61 b([)13 b(])1688 1775 y Fn(\031)1735 1784
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5186
y Fg(\001)1773 1775 y Fw(\()p Fn(h)22 b Fw(::)g Fn(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5187
Fw(\))2038 1732 y Fy(def)2051 1775 y Fw(=)61 b(\()p Fn(\031)2249
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5188
1784 y Fg(\001)2286 1775 y Fn(h)p Fw(\))22 b(::)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5189
Fn(\031)2523 1784 y Fg(\001)2560 1775 y Fn(t)p Fw(\))1218
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5190
1894 y(tuples:)71 b Fn(\031)1558 1903 y Fg(\001)1596
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5191
1894 y Fw(\()p Fn(x)1670 1902 y Fx(1)1704 1894 y Fn(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5192
b(:)g(:)g(:)g(;)g(x)1918 1902 y Fi(n)1960 1894 y Fw(\))2038
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5193
1851 y Fy(def)2051 1894 y Fw(=)61 b(\()p Fn(\031)2249
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5194
1903 y Fg(\001)2286 1894 y Fn(x)2330 1902 y Fx(1)2364
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5195
1894 y Fn(;)14 b(:)f(:)g(:)g(;)g(\031)2582 1903 y Fg(\001)2620
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5196
1894 y Fn(x)2664 1902 y Fi(n)2706 1894 y Fw(\))3307 1762
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5197
y(\(5\))523 2053 y Fz(F)-7 b(urther,)28 b(on)f Fr(\013)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5198
Fz(-equated)g Fr(\025)p Fz(-terms)h(w)n(e)f(can)g(de\014ne)h(the)g(p)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5199
(erm)n(utation)f(action:)1528 2236 y Fn(\031)1575 2245
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5200
y Fg(\001)1613 2236 y Fk(var)9 b Fw(\()p Fn(x)p Fw(\))1878
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5201
2193 y Fy(def)1892 2236 y Fw(=)60 b Fk(var)9 b Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5202
Fn(\031)2204 2245 y Fg(\001)2242 2236 y Fn(x)p Fw(\))1312
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5203
2378 y Fn(\031)1359 2387 y Fg(\001)1397 2378 y Fk(app)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5204
Fw(\()p Fn(M)1624 2386 y Fx(1)1658 2378 y Fn(;)13 b(M)1766
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5205
2386 y Fx(2)1801 2378 y Fw(\))1878 2335 y Fy(def)1892
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5206
2378 y Fw(=)60 b Fk(app)6 b Fw(\()p Fn(\031)2212 2387
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5207
y Fg(\001)2249 2378 y Fn(M)2323 2386 y Fx(1)2358 2378
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5208
y Fn(;)13 b(\031)2439 2387 y Fg(\001)2477 2378 y Fn(M)2551
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5209
2386 y Fx(2)2586 2378 y Fw(\))1412 2520 y Fn(\031)1459
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5210
2529 y Fg(\001)1497 2520 y Fk(lam)5 b Fw(\()p Fn(x:M)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5211
Fw(\))1878 2478 y Fy(def)1892 2520 y Fw(=)60 b Fk(lam)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5212
b Fw(\()p Fn(\031)2217 2529 y Fg(\001)2254 2520 y Fn(x:\031)2366
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5213
2529 y Fg(\001)2404 2520 y Fn(M)i Fw(\))3307 2365 y(\(6\))648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5214
2685 y Fz(The)39 b(second)g(notion)g(that)h(w)n(e)f(use)g(is)h(that)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5215
(of)h Fs(supp)l(ort)47 b Fz(\(roughly)39 b(sp)r(eaking,)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5216
2784 y(supp)r(ort)32 b(of)g(an)g(elemen)n(t)g(is)g(its)g(set)g(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5217
(free)g(atoms\).)f(The)i(set)f(supp)r(orting)f(an)h(elemen)n(t)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5218
2884 y(is)g(de\014ned)g(in)g(terms)f(of)h(p)r(erm)n(utation)f(actions)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5219
(on)h(that)g(elemen)n(t,)g(so)f(that)h(as)f(so)r(on)g(as)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5220
2984 y(one)h(has)f(de\014ned)i(a)f(p)r(erm)n(utation)g(action)f(for)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5221
(a)g(t)n(yp)r(e,)g(one)g(automatically)f(deriv)n(es)g(its)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5222
3083 y(accompan)n(ying)17 b(notion)h(of)h(supp)r(ort,)f(whic)n(h)h(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5223
(turn)f(determines)h(the)g(notion)f(of)h(freshness)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5224
3183 y(\(see)28 b([11]\):)p Black 523 3336 a Ft(De\014nition)j(3)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5225
Black 41 w(\(Supp)s(ort)49 b(and)g(F)-8 b(reshness\).)47
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5226
b Fs(The)j Fz(supp)r(ort)43 b Fs(of)h Fr(x)f Fs(is)h(de\014ne)l(d)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5227
(as:)523 3465 y Fe(supp)n Fz(\()p Fr(x)p Fz(\))849 3414
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5228
y Fd(def)861 3465 y Fz(=)51 b Fp(f)p Fr(a)39 b Fp(j)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5229
Fe(infinite)m Fp(f)p Fr(b)f Fp(j)h Fz(\()p Fr(a)14 b(b)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5230
Fz(\))1852 3474 y Fg(\001)1890 3465 y Fr(x)40 b Fp(6)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5231
Fz(=)f Fr(x)p Fp(gg)p Fs(.)g(A)n(n)f(atom)i Fr(a)e Fs(is)i(said)g(to)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5232
(b)l(e)45 b Fz(fresh)523 3565 y Fs(for)31 b(an)e Fr(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5233
Fs(,)i(written)e Fr(a)23 b Fz(#)h Fr(x)p Fs(,)30 b(if)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5234
Fr(a)23 b Fp(62)g Fe(supp)o Fz(\()p Fr(x)p Fz(\))p Fs(.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5235
3718 y Fz(W)-7 b(e)23 b(will)f(also)f(use)h(the)g(auxiliary)f(notation)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5236
h Fr(a)h Fz(#)g Fs(xs)6 b Fz(,)23 b(in)f(whic)n(h)g Fs(xs)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5237
b Fz(stands)21 b(for)h(a)g(collection)523 3818 y(of)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5238
b(ob)5 b(jects)27 b Fr(x)949 3830 y Fy(1)1001 3818 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5239
Fr(:)14 b(:)g(:)f(x)1158 3830 y Fq(n)1204 3818 y Fz(,)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5240
b(to)g(mean)f Fr(a)d Fz(#)g Fr(x)1786 3830 y Fy(1)1837
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5241
3818 y Fr(:)14 b(:)g(:)g(a)23 b Fz(#)h Fr(x)2155 3830
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5242
y Fq(n)2200 3818 y Fz(.)k(W)-7 b(e)29 b(further)f(generalise)e(this)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5243
(nota-)523 3917 y(tion)d(to)g(a)g(collection)g(of)g(atoms,)f(namely)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5244
Fs(as)30 b Fz(#)24 b Fs(xs)6 b Fz(,)25 b(whic)n(h)g(means)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5245
Fr(a)2724 3929 y Fy(1)2784 3917 y Fz(#)f Fs(xs)c Fr(:)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5246
b(:)g(:)f(a)3124 3929 y Fq(m)3210 3917 y Fz(#)24 b Fs(xs)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5247
b Fz(.)648 4017 y(Later)26 b(on)h(w)n(e)g(will)g(often)h(mak)n(e)e(use)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5248
h(of)g(the)h(follo)n(wing)e(t)n(w)n(o)g(prop)r(erties)h(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5249
(freshness,)523 4117 y(whic)n(h)h(can)f(b)r(e)h(deriv)n(ed)f(from)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5250
(the)h(de\014nition)g(of)f(supp)r(ort,)h(the)g(p)r(erm)n(utation)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5251
(action)g(on)523 4216 y Fh(A)51 b Fz(and)27 b(the)h(requiremen)n(ts)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5252
(of)g(p)r(erm)n(utation)g(actions)g(on)h(other)f(t)n(yp)r(es)g(\(see)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5253
([11]\).)p Black 523 4370 a Ft(Lemma)i(1.)p Black Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5254
581 4465 a Fp(\017)p Black 41 w Fz(\()p Fr(a)p Fz(\))53
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5255
b Fr(a)23 b Fz(#)h Fr(x)30 b Fs(implies)h Fr(\031)1396
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5256
4474 y Fg(\001)1435 4465 y Fr(a)22 b Fz(#)i Fr(\031)1644
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5257
4474 y Fg(\001)1682 4465 y Fr(x)p Fs(;)31 b(and)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5258
581 4563 a Fp(\017)p Black 41 w Fz(\()p Fr(b)p Fz(\))53
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5259
b Fs(if)31 b Fr(a)23 b Fz(#)g Fr(x)30 b Fs(and)g Fr(b)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5260
b Fz(#)g Fr(x)p Fs(,)31 b(then)e Fz(\()p Fr(a)14 b(b)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5261
Fz(\))1891 4572 y Fg(\001)1930 4563 y Fr(x)23 b Fz(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5262
Fr(x)p Fs(.)523 4725 y Fz(Henceforth)h(w)n(e)g(will)h(only)e(b)r(e)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5263
(in)n(terested)f(in)g(those)g(ob)5 b(jects)24 b(whic)n(h)g(ha)n(v)n(e)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5264
(\014nite)i(supp)r(ort,)523 4825 y(b)r(ecause)k(for)g(them)h(there)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5265
(exists)f(alw)n(a)n(ys)e(a)j(fresh)f(atom)g(\(recall)g(that)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5266
(set)f(of)h(atoms)523 4924 y Fh(A)51 b Fz(is)27 b(in\014nite\).)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5267
Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5268
%%Page: 7 7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5269
TeXDict begin 7 6 bop Black 1347 232 a Fw(Barendregt's)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5270
b(V)-6 b(ariable)26 b(Con)n(v)n(en)n(tion)f(in)h(Rule)f(Inductions)237
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5271
b(7)p Black Black 523 448 a Ft(Lemma)30 b(2.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5272
40 w Fs(If)22 b Fr(x)g Fs(is)g(\014nitely)f(supp)l(orte)l(d,)h(then)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5273
(ther)l(e)h(exists)f(an)g(atom)h Fr(a)f Fs(such)g(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5274
Fr(a)h Fz(#)g Fr(x)p Fs(.)523 601 y Fz(Un)n(winding)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5275
b(the)g(de\014nitions)g(of)f(p)r(erm)n(utation)h(actions)e(and)i(supp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5276
(ort)f(one)g(can)h(often)523 701 y(easily)27 b(calculate)g(the)h(supp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5277
(ort)f(of)h(an)f(ob)5 b(ject:)p Black Black 833 850 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5278
Fw(atoms:)492 b Fc(supp)q Fw(\()p Fn(a)p Fw(\))21 b(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5279
Fm(f)p Fn(a)p Fm(g)833 965 y Fw(tuples:)492 b Fc(supp)q
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5280
Fw(\()p Fn(x)1778 973 y Fx(1)1812 965 y Fn(;)13 b(:)g(:)g(:)g(;)g(x)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5281
2026 973 y Fi(n)2068 965 y Fw(\))22 b(=)f Fc(supp)q Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5282
Fn(x)2432 973 y Fx(1)2466 965 y Fw(\))c Fm([)g Fn(:)c(:)g(:)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5283
Fm([)h Fc(supp)q Fw(\()p Fn(x)2987 973 y Fi(n)3028 965
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5284
y Fw(\))833 1080 y(lists:)561 b Fc(supp)q Fw(\([)13 b(]\))21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5285
b(=)g Fb(?)p Fw(,)26 b Fc(supp)q Fw(\()p Fn(h)21 b Fw(::)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5286
Fn(t)p Fw(\))f(=)g Fc(supp)q Fw(\()p Fn(h)p Fw(\))c Fm([)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5287
Fc(supp)p Fw(\()p Fn(t)p Fw(\))833 1195 y Fn(\013)p Fw(-equated)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5288
b Fn(\025)p Fw(-terms:)70 b Fc(supp)q Fw(\()p Fk(var)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5289
b Fw(\()p Fn(x)p Fw(\)\))20 b(=)h Fm(f)p Fn(x)p Fm(g)1547
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5290
1287 y Fc(supp)q Fw(\()p Fk(app)5 b Fw(\()p Fn(M)t(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5291
b(N)8 b Fw(\)\))21 b(=)h Fc(supp)p Fw(\()p Fn(M)8 b Fw(\))18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5292
b Fm([)f Fc(supp)q Fw(\()p Fn(N)8 b Fw(\))1547 1378 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5293
Fc(supp)q Fw(\()p Fk(lam)d Fw(\()p Fn(x:M)j Fw(\)\))21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5294
b(=)g Fc(supp)q Fw(\()p Fn(M)8 b Fw(\))17 b Fm(\000)g(f)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5295
Fn(x)p Fm(g)523 1533 y Fz(W)-7 b(e)25 b(therefore)f(note)h(the)g(follo)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5296
n(wing:)e(all)i(elemen)n(ts)f(in)h Fh(A)48 b Fz(and)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5297
b(all)f Fr(\013)p Fz(-equated)g Fr(\025)p Fz(-terms)h(are)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5298
1632 y(\014nitely)d(supp)r(orted.)g(Lists)g(\(similarly)f(tuples\))i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5299
(con)n(taining)e(\014nitely)h(supp)r(orted)g(elemen)n(ts)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5300
1732 y(are)37 b(\014nitely)i(supp)r(orted.)f(The)g(last)g(three)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5301
(equations)f(sho)n(w)h(that)g(the)h(supp)r(ort)f(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5302
Fr(\013)p Fz(-)523 1832 y(equated)24 b Fr(\025)p Fz(-terms)g(coincides)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5303
g(with)h(the)g(usual)f(notion)g(of)g(free)g(v)-5 b(ariables.)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5304
b(Hence,)g Fr(a)f Fz(#)g Fr(M)523 1931 y Fz(with)k Fr(M)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5305
b Fz(b)r(eing)27 b(an)f Fr(\013)p Fz(-equated)h Fr(\025)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5306
Fz(-term)g(coincides)f(with)i Fr(a)e Fz(not)h(b)r(eing)g(free)g(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5307
Fr(M)9 b Fz(.)26 b(If)i Fr(b)e Fz(is)523 2031 y(an)h(atom,)h(then)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5308
Fr(a)23 b Fz(#)g Fr(b)k Fz(coincides)g(with)h Fr(a)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5309
b Fp(6)p Fz(=)g Fr(b)p Fz(.)648 2130 y(The)k(last)h(notion)f(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5310
(nominal)h(logic)e(w)n(e)i(use)f(here)g(is)h(that)f(of)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5311
Fs(e)l(quivarianc)l(e)p Fz(.)p Black 523 2283 a Ft(De\014nition)j(4)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5312
Black 41 w(\(Equiv)-5 b(ariance\).)p Black 581 2377 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5313
Fp(\017)p Black 41 w Fs(A)30 b(r)l(elation)g Fr(R)g Fs(is)37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5314
b Fz(equiv)-5 b(arian)n(t)29 b Fs(if)h Fr(R)15 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5315
Fr(\031)1923 2386 y Fg(\001)1962 2377 y Fs(xs)6 b Fz(\))30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5316
b Fs(is)g(implie)l(d)i(by)e Fr(R)14 b Fs(xs)36 b(for)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5317
b(al)t(l)g Fr(\031)s Fs(.)p Black 581 2476 a Fp(\017)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5318
Black 41 w Fs(A)f(function)f Fr(f)39 b Fs(is)e Fz(equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5319
b(arian)n(t)28 b Fs(pr)l(ovide)l(d)k Fr(\031)2069 2485
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5320
y Fg(\001)2107 2476 y Fz(\()p Fr(f)23 b Fs(xs)6 b Fz(\))24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5321
b(=)e Fr(f)h Fz(\()p Fr(\031)2571 2485 y Fg(\001)2610
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5322
2476 y Fs(xs)6 b Fz(\))30 b Fs(for)g(al)t(l)h Fr(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5323
Fs(.)p Black 523 2690 a(R)l(emark)f(1.)p Black 42 w Fz(Note)35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5324
b(that)g(if)g(w)n(e)f(regard)f(the)i(term-constructors)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5325
Fs(var)10 b Fz(,)34 b Fs(app)42 b Fz(and)34 b Fs(lam)42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5326
b Fz(as)523 2789 y(functions,)35 b(then)g(they)g(are)e(equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5327
b(arian)n(t)34 b(on)g(accoun)n(t)g(of)g(the)h(de\014nition)g(giv)n(en)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5328
(in)h(\(6\).)523 2889 y(Because)e(of)h(the)h(de\014nition)g(in)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5329
(\(5\),)g(the)h(cons-constructors)c(of)k(lists)f(are)f(equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5330
b(arian)n(t.)523 2989 y(By)27 b(a)g(simple)h(structural)e(induction)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5331
(on)g(the)f(list)h(argumen)n(t)e(of)i Fs(valid)p Fz(,)h(w)n(e)e(can)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5332
(establish)523 3088 y(that)c(the)h(relation)e Fs(valid)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5333
b Fz(is)23 b(equiv)-5 b(arian)n(t.)22 b(By)h(Lem.)g(1\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5334
Fr(a)p Fz(\))g(freshness)f(is)h(equiv)-5 b(arian)n(t.)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5335
b(Also)523 3188 y(list-mem)n(b)r(ership,)j(\()p Fp(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5336
Fz(\))f Fp(2)f Fz(\()p Fp(\000)p Fz(\),)j(is)f(equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5337
b(arian)n(t,)24 b(whic)n(h)i(can)f(b)r(e)h(sho)n(wn)e(b)n(y)h(an)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5338
(induction)523 3287 y(on)h(the)h(length)g(of)g(lists.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5339
3548 y Fu(3)112 b(Sc)m(hematic)36 b(T)-9 b(erms)37 b(and)h(Sc)m
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5340
(hematic)e(Rules)523 3734 y Fz(Inductiv)n(e)18 b(relations)g(are)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5341
(de\014ned)i(as)e(the)i(smallest)f(relation)g(closed)f(under)i(some)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5342
(sc)n(hematic)523 3825 y(rules.)31 b(In)h(this)g(section)f(w)n(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5343
(will)h(formally)f(sp)r(ecify)g(the)h(form)g(of)f(suc)n(h)g(rules.)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5344
(Diagram-)523 3917 y(matically)27 b(they)h(ha)n(v)n(e)e(the)i(form)1493
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5345
4058 y Fk(pr)l(emises)78 b(side-c)l(onditions)p 1493
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5346
4093 860 4 v 1750 4161 a(c)l(onclusion)2395 4102 y Fn(\045)3307
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5347
4161 y Fw(\(7\))523 4327 y Fz(where)31 b(the)h(premises,)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5348
(side-conditions)g(and)h(conclusions)e(are)h(predicates)g(of)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5349
(form)523 4426 y Fr(R)15 b Fs(ts)28 b Fz(where)22 b(w)n(e)g(use)h(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5350
(letters)h Fr(R)q Fz(,)f Fr(S)5 b Fz(,)22 b Fr(P)34 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5351
Fz(and)23 b Fr(Q)f Fz(to)g(stand)g(for)g(predicates;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5352
Fs(ts)29 b Fz(stands)22 b(for)523 4526 y(a)k(collection)g(of)h(sc)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5353
(hematic)f(terms)g(\(the)h(argumen)n(ts)f(of)g Fr(R)q
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5354
Fz(\).)h(They)f(are)g(either)g(v)-5 b(ariables,)523 4625
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5355
y(abstractions)36 b(or)g(functions,)i(namely)77 b Fr(t)40
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5356
b Fz(::=)f Fr(x)h Fp(j)f Fr(a:t)h Fp(j)f Fr(f)23 b Fs(ts)83
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5357
b Fz(where)37 b Fr(a)h Fz(is)f(a)g(v)-5 b(ariable)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5358
4725 y(standing)29 b(for)g(an)h(atom)f(and)g Fr(f)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5359
b Fz(stands)29 b(for)g(a)g(function.)i(W)-7 b(e)30 b(call)f(the)h(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5360
b(ariable)28 b Fr(a)i Fz(in)g Fr(a:t)523 4825 y Fz(as)g(b)r(eing)h(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5361
Fs(binding)j(p)l(osition)p Fz(.)e(Note)e(that)i(a)e(sc)n(hematic)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5362
(rule)g(ma)n(y)g(con)n(tain)g(the)i(same)523 4924 y(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5363
b(ariable)27 b(in)g(binding)h(and)g(non-binding)f(p)r(ositions)g(\(One)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5364
2383 4936 y Fy(4)2448 4924 y Fz(and)g(T)n(yp)r(e)2796
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5365
4936 y Fy(3)2861 4924 y Fz(are)g(examples\).)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5366
Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5367
%%Page: 8 8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5368
TeXDict begin 8 7 bop Black 523 232 a Fw(8)237 b(Christian)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5369
b(Urban,)e(Stefan)h(Berghofer,)i(and)d(Mic)n(hael)i(Norrish)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5370
Black 648 448 a Fz(Assuming)33 b(an)f(inductiv)n(e)i(de\014nition)f(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5371
g(the)h(predicate)e Fr(R)q Fz(,)h(the)g(sc)n(hematic)g(rule)g(in)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5372
540 y(\(7\))28 b(m)n(ust)g(b)r(e)g(of)f(the)h(form)1352
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5373
692 y Fn(R)13 b Fk(ts)1486 700 y Fx(1)1555 692 y Fn(:)g(:)g(:)35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5374
b(R)13 b Fk(ts)1813 700 y Fi(n)1919 692 y Fn(S)1966 700
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5375
y Fx(1)2001 692 y Fk(ss)2070 700 y Fx(1)2138 692 y Fn(:)h(:)f(:)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5376
b(S)2309 700 y Fi(m)2368 692 y Fk(ss)2437 700 y Fi(m)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5377
1352 721 1144 4 v 1856 788 a Fn(R)14 b Fk(ts)2537 729
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5378
y Fn(\045)3307 788 y Fw(\(8\))523 960 y Fz(where)k(the)h(predicates)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5379
Fr(S)1322 972 y Fq(i)1350 960 y Fs(ss)1424 972 y Fq(i)1471
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5380
960 y Fz(\(the)i(ones)e(di\013eren)n(t)i(from)f Fr(R)q
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5381
Fz(\))g(stand)g(for)g(the)h(side-conditions)523 1060
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5382
y(in)28 b(the)g(sc)n(hematic)f(rule.)648 1152 y(F)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5383
b(or)26 b(pro)n(ving)g(our)h(main)g(result)g(in)h(the)g(next)g(section)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5384
f(it)g(is)h(con)n(v)n(enien)n(t)e(to)h(in)n(tro)r(duce)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5385
1243 y(sev)n(eral)f(auxiliary)g(notions)g(for)h(sc)n(hematic)g(terms)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5386
(and)g(rules.)g(The)g(follo)n(wing)g(functions)523 1335
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5387
y(calculate)j(for)h(a)f(sc)n(hematic)h(term)g(the)g(set)g(of)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5388
b(ariables)30 b(in)h(non-binding)f(p)r(osition)h(and)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5389
1426 y(the)d(set)g(of)f(v)-5 b(ariables)26 b(in)i(binding)g(p)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5390
(osition,)g(resp)r(ectiv)n(ely:)995 1587 y Fk(vars)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5391
b Fw(\()p Fn(x)p Fw(\))23 b(=)e Fm(f)p Fn(x)p Fm(g)948
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5392
1678 y Fk(vars)8 b Fw(\()p Fn(a:t)p Fw(\))23 b(=)e Fk(vars)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5393
b Fw(\()p Fn(t)p Fw(\))t Fm(\000)t(f)p Fn(a)p Fm(g)917
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5394
1769 y Fk(vars)g Fw(\()p Fn(f)21 b Fk(ts)7 b Fw(\))24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5395
b(=)d Fk(vars)7 b Fw(\()p Fk(ts)g Fw(\))2078 1587 y Fk(varsbp)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5396
Fw(\()p Fn(x)p Fw(\))23 b(=)e Fb(?)2032 1678 y Fk(varsbp)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5397
b Fw(\()p Fn(a:t)p Fw(\))23 b(=)e Fk(varsbp)7 b Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5398
Fn(t)p Fw(\))16 b Fm([)i(f)p Fn(a)p Fm(g)2000 1769 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5399
Fk(varsbp)7 b Fw(\()p Fn(f)21 b Fk(ts)7 b Fw(\))23 b(=)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5400
Fk(varsbp)7 b Fw(\()p Fk(ts)g Fw(\))3307 1679 y(\(9\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5401
1941 y Fz(The)26 b(notation)f Fr(t)p Fz([)p Fs(as)7 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5402
Fz(;)14 b Fs(xs)6 b Fz(])26 b(will)g(b)r(e)g(used)g(for)f(sc)n(hematic)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5403
g(terms)h(to)f(indicate)h(that)g(the)g(v)-5 b(ari-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5404
2040 y(ables)27 b(in)h(binding)g(p)r(osition)f(of)h Fr(t)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5405
Fz(are)f(included)h(in)g Fs(as)35 b Fz(and)27 b(the)h(other)f(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5406
b(ariables)27 b(of)g Fr(t)h Fz(are)523 2140 y(either)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5407
b(in)g Fs(as)43 b Fz(or)35 b Fs(xs)7 b Fz(.)36 b(That)g(means)f(w)n(e)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5408
(ha)n(v)n(e)e(for)i Fr(t)p Fz([)p Fs(as)7 b Fz(;)14 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5409
Fs(xs)6 b Fz(])36 b(that)g Fs(varsbp)7 b Fz(\()p Fr(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5410
Fz(\))37 b Fp(\022)g Fs(as)43 b Fz(and)523 2239 y Fs(vars)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5411
b Fz(\()p Fr(t)p Fz(\))24 b Fp(\022)f Fs(as)i Fp([)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5412
b Fs(xs)34 b Fz(hold.)523 2331 y(W)-7 b(e)30 b(extend)h(this)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5413
(notation)f(also)g(to)h(sc)n(hematic)g(rules:)f(b)n(y)h(writing)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5414
Fr(\045)p Fz([)p Fs(as)7 b Fz(;)14 b Fs(xs)7 b Fz(])30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5415
b(for)f(\(8\))h(w)n(e)523 2423 y(mean)880 2568 y Fn(R)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5416
b Fk(ts)1014 2576 y Fx(1)1049 2568 y Fw([)p Fk(as)7 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5417
Fw(;)13 b Fk(xs)7 b Fw(])34 b Fn(:)13 b(:)h(:)34 b(R)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5418
b Fk(ts)1567 2576 y Fi(n)1610 2568 y Fw([)p Fk(as)7 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5419
Fw(;)13 b Fk(xs)7 b Fw(])77 b Fn(S)1960 2576 y Fx(1)2007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5420
2568 y Fk(ss)2076 2576 y Fx(1)2111 2568 y Fw([)p Fk(as)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5421
b Fw(;)13 b Fk(xs)7 b Fw(])34 b Fn(:)13 b(:)g(:)35 b(S)2542
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5422
2576 y Fi(m)2613 2568 y Fk(ss)2682 2576 y Fi(m)2741 2568
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5423
y Fw([)p Fk(as)7 b Fw(;)13 b Fk(xs)7 b Fw(])p 868 2615
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5424
2111 4 v 1743 2688 a Fn(R)14 b Fk(ts)6 b Fw([)p Fk(as)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5425
Fw(;)14 b Fk(xs)6 b Fw(])3020 2624 y Fn(\045)3268 2688
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5426
y Fw(\(10\))523 2860 y Fz(Ho)n(w)n(ev)n(er,)18 b(unlik)n(e)h(in)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5427
(notation)f(for)g(sc)n(hematic)g(terms,)g(w)n(e)g(mean)g(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5428
Fr(\045)p Fz([)p Fs(as)7 b Fz(;)14 b Fs(xs)6 b Fz(])20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5429
b(that)g(the)523 2960 y Fs(as)36 b Fz(stand)28 b Fs(exactly)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5430
b Fz(for)28 b(the)g(v)-5 b(ariables)27 b(o)r(ccurring)g(somewhere)g(in)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5431
i Fr(\045)f Fz(in)h(binding)f(p)r(osition)523 3060 y(and)e(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5432
Fs(xs)32 b Fz(stand)26 b(for)g(the)h(rest)e(of)i(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5433
b(ariables.)25 b(That)h(means)f(w)n(e)h(ha)n(v)n(e)f(for)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5434
Fr(\045)p Fz([)p Fs(as)7 b Fz(;)14 b Fs(xs)6 b Fz(])27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5435
b(that)523 3159 y Fs(varsbp)6 b Fz(\()p Fr(\045)p Fz(\))27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5436
b(=)f Fs(as)37 b Fz(and)29 b Fs(vars)7 b Fz(\()p Fr(\045)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5437
Fz(\))27 b(=)f Fs(xs)36 b Fz(hold,)29 b(assuming)g(suitable)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5438
(generalisations)e(of)j(the)523 3259 y(functions)24 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5439
Fs(vars)31 b Fz(and)24 b Fs(varsbp)30 b Fz(to)23 b(sc)n(hematic)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5440
(rules.)f(T)-7 b(o)23 b(see)g(ho)n(w)g(the)h(sc)n(hematic)g(notation)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5441
523 3358 y(w)n(orks)h(out)i(in)g(examples,)f(reconsider)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5442
(de\014nitions)g(for)f(the)h(relations)f(One,)h(giv)n(en)f(in)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5443
3458 y(\(1\),)h(and)f(T)n(yp)r(e,)g(giv)n(en)g(in)g(\(2\).)h(Using)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5444
(our)g(sc)n(hematic)g(notation)g(for)f(the)i(rules,)f(w)n(e)g(ha)n(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5445
(e)p Black Black 1079 3620 a Fw(One)1216 3628 y Fx(1)1250
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5446
3620 y Fw([)p Fm(\000)p Fw(;)13 b Fn(M)8 b Fw(])1079
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5447
3711 y(One)1216 3719 y Fx(2)1250 3711 y Fw([)p Fn(y)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5448
Fw(;)13 b Fn(M)t(;)g(M)1540 3680 y Fl(0)1563 3711 y Fw(])1079
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5449
3803 y(One)1216 3811 y Fx(3)1250 3803 y Fw([)p Fm(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5450
Fw(;)g Fn(M)t(;)h(N)t(;)f(M)1659 3771 y Fl(0)1682 3803
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5451
y Fn(;)g(N)1785 3771 y Fl(0)1807 3803 y Fw(])1079 3894
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5452
y(One)1216 3902 y Fx(4)1250 3894 y Fw([)p Fn(y)s Fw(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5453
Fn(M)t(;)g(N)t(;)h(M)1640 3862 y Fl(0)1662 3894 y Fn(;)f(N)1765
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5454
3862 y Fl(0)1788 3894 y Fw(])2017 3620 y(T)n(yp)r(e)2190
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5455
3639 y Fx(1)2225 3620 y Fw([)p Fm(\000)p Fw(;)g Fn(\000)r(;)g(x;)g(T)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5456
Fw(])2017 3711 y(T)n(yp)r(e)2190 3730 y Fx(2)2225 3711
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5457
y Fw([)p Fm(\000)p Fw(;)i Fn(\000)r(;)g(M)t(;)g(N)t(;)h(T)2680
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5458
3719 y Fx(1)2714 3711 y Fn(;)f(T)2793 3719 y Fx(2)2828
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5459
3711 y Fw(])2017 3803 y(T)n(yp)r(e)2190 3821 y Fx(3)2225
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5460
3803 y Fw([)p Fn(x)p Fw(;)g Fn(\000)r(;)g(M)t(;)g(T)2564
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5461
3811 y Fx(1)2598 3803 y Fn(;)h(T)2678 3811 y Fx(2)2712
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5462
3803 y Fw(])523 4056 y Fz(where)27 b(`)p Fp(\000)p Fz(')g(stands)h(for)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5463
f(no)g(v)-5 b(ariable)27 b(in)g(binding)h(p)r(osition.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5464
4148 y(The)d(main)g(prop)r(ert)n(y)f(of)h(an)g(inductiv)n(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5465
(de\014nition,)g(sa)n(y)f(for)h(the)g(inductiv)n(e)h(predicate)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5466
4239 y Fr(R)q Fz(,)36 b(is)h(that)g(it)g(comes)f(with)h(an)f(induction)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5467
h(principle,)g(whic)n(h)f(establishes)g(a)g(prop)r(ert)n(y)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5468
4330 y Fr(P)26 b Fs(ts)41 b Fz(under)34 b(the)h(assumption)f(that)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5469
Fr(R)15 b Fs(ts)41 b Fz(holds.)34 b(This)g(means)g(w)n(e)g(ha)n(v)n(e)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5470
(an)i(induction)523 4422 y(principle)28 b(diagrammatically)d(lo)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5471
(oking)i(as)g(follo)n(ws)959 4583 y Fn(:)13 b(:)g(:)959
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5472
4674 y Fm(8)p Fk(as)19 b(xs)7 b Fn(:)22 b(P)11 b Fk(ts)1329
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5473
4682 y Fx(1)1364 4674 y Fw([)p Fk(as)c Fw(;)13 b Fk(xs)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5474
b Fw(])39 b Fm(^)f Fn(:)13 b(:)h(:)38 b Fm(^)h Fn(P)11
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5475
b Fk(ts)2059 4682 y Fi(n)2101 4674 y Fw([)p Fk(as)c Fw(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5476
b Fk(xs)7 b Fw(])22 b Fm(^)1314 4765 y Fn(S)t Fk(ss)1434
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5477
4773 y Fx(1)1468 4765 y Fw([)p Fk(as)7 b Fw(;)13 b Fk(xs)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5478
b Fw(])39 b Fm(^)f Fn(:)14 b(:)f(:)38 b Fm(^)h Fn(S)t
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5479
Fk(ss)2160 4773 y Fi(m)2219 4765 y Fw([)p Fk(as)7 b Fw(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5480
b Fk(xs)7 b Fw(])43 b Fm(\))f Fn(P)24 b Fk(ts)6 b Fw([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5481
Fk(as)h Fw(;)14 b Fk(xs)6 b Fw(])959 4809 y Fn(:)13 b(:)g(:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5482
948 4857 2033 4 v 1769 4924 a(R)h Fk(ts)28 b Fm(\))21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5483
b Fn(P)j Fk(ts)1116 b Fw(\(11\))p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5484
%%Page: 9 9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5485
TeXDict begin 9 8 bop Black 1347 232 a Fw(Barendregt's)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5486
b(V)-6 b(ariable)26 b(Con)n(v)n(en)n(tion)f(in)h(Rule)f(Inductions)237
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5487
b(9)p Black 523 448 a Fz(where)26 b(for)f(ev)n(ery)g(sc)n(hematic)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5488
(rule)h Fr(\045)g Fz(in)g(the)g(inductiv)n(e)h(de\014nition)f(w)n(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5489
(ha)n(v)n(e)e(to)i(establish)523 548 y(an)34 b(implication.)h(These)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5490
(implications)h(state)f(that)h(w)n(e)f(can)g(assume)g(the)h(prop)r(ert)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5491
n(y)f(for)523 648 y(all)25 b(premises)g(and)h(also)e(can)i(assume)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5492
(that)i(the)g(side-conditions)f(hold;)h(w)n(e)f(ha)n(v)n(e)f(to)i(sho)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5493
(w)523 747 y(that)i(the)g(prop)r(ert)n(y)e(holds)i(for)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5494
(conclusion)e(of)i(the)g(sc)n(hematic)f(rule.)648 849
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5495
y(As)40 b(explained)f(in)h(the)h(in)n(tro)r(duction,)e(w)n(e)h(need)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5496
(to)g(imp)r(ose)g(some)f(conditions)g(on)523 949 y(sc)n(hematic)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5497
b(rules)f(in)i(order)e(to)h(a)n(v)n(oid)f(fault)n(y)h(reasoning)e(and)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5498
(to)g(p)r(ermit)h(an)f(argumen)n(t)523 1048 y(emplo)n(ying)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5499
b(the)i(v)-5 b(ariable)28 b(con)n(v)n(en)n(tion.)g(A)h(rule)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5500
Fr(\045)p Fz([)p Fs(as)7 b Fz(;)14 b Fs(xs)6 b Fz(],)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5501
b(as)e(giv)n(en)g(in)i(\(10\),)f(is)g Fs(variable)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5502
1148 y(c)l(onvention)22 b(c)l(omp)l(atible)p Fz(,)f(short)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5503
Fs(vc-c)l(omp)l(atible)p Fz(,)i(pro)n(vided)e(the)i(follo)n(wing)d(t)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5504
(w)n(o)h(conditions)523 1247 y(are)27 b(satis\014ed.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5505
Black 523 1432 a Ft(De\014nition)k(5)p Black 41 w(\(V)-8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5506
b(ariable)37 b(Con)m(v)m(en)m(tion)g(Compatibilit)m(y\).)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5507
Fs(A)f(rule)g Fr(\045)p Fz([)p Fs(as)8 b Fz(;)14 b Fs(xs)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5508
b Fz(])33 b Fs(with)523 1532 y(c)l(onclusion)d Fr(R)15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5509
b Fs(ts)36 b(is)h Fz(v)n(c-compatible)28 b Fs(pr)l(ovide)l(d)k(that:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5510
Black 581 1706 a Fp(\017)p Black 41 w Fs(al)t(l)f(functions)f(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5511
(side-c)l(onditions)h(o)l(c)l(curring)f(in)g Fr(\045)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5512
Fs(ar)l(e)g(e)l(quivariant,)h(and)p Black 581 1808 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5513
Fp(\017)p Black 41 w Fs(the)f(side-c)l(onditions)i Fr(S)1420
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5514
1820 y Fy(1)1457 1808 y Fs(ss)1531 1820 y Fy(1)1587 1808
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5515
y Fp(^)19 b Fr(:)14 b(:)g(:)k Fp(^)h Fr(S)1901 1820 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5516
Fq(m)1964 1808 y Fs(ss)2039 1820 y Fq(m)2131 1808 y Fs(imply)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5517
b(that)f(as)g Fz(#)24 b Fs(ts)36 b(holds)31 b(and)664
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5518
1908 y(that)f(the)g(as)37 b(ar)l(e)30 b(distinct.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5519
2090 y Fz(If)d(ev)n(ery)f(sc)n(hematic)g(rule)g(in)i(an)e(inductiv)n(e)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5520
h(de\014nition)g(satis\014es)f(these)h(conditions,)f(then)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5521
2190 y(the)35 b(induction)g(principle)f(can)g(b)r(e)h(strengthened)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5522
(suc)n(h)g(that)h(it)g(includes)f(a)g(v)n(ersion)f(of)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5523
2289 y(the)28 b(v)-5 b(ariable)27 b(con)n(v)n(en)n(tion.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5524
2566 y Fu(4)112 b(Strengthening)37 b(of)h(the)f(Induction)g(Principle)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5525
523 2767 y Fz(In)32 b(this)g(section)f(w)n(e)g(will)h(sho)n(w)f(ho)n(w)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5526
g(to)g(obtain)g(a)h(stronger)d(induction)j(principle)g(than)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5527
2858 y(the)e(one)f(giv)n(en)f(in)i(\(11\).)f(By)g(stronger)e(w)n(e)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5528
(mean)g(that)h(it)g(has)f(the)g(v)-5 b(ariable)28 b(con)n(v)n(en)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5529
(tion)523 2950 y(already)i(built)j(in)f(\(this)g(will)g(then)h(enable)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5530
(us)h(to)g(giv)n(e)e(slic)n(k)i(pro)r(ofs)f(b)n(y)g(rule)h(induction)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5531
523 3041 y(whic)n(h)f(do)g(not)g(need)g(an)n(y)f(renaming\).)h(F)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5532
b(ormally)30 b(w)n(e)g(sho)n(w)h(that)g(induction)g(principles)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5533
3132 y(of)d(the)g(form)651 3281 y Fn(:)13 b(:)g(:)651
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5534
3373 y Fm(8)p Fk(as)19 b(xs)h Fn(C)q(:)h Fw(\()p Fm(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5535
Fn(C)q(:P)i(C)18 b Fk(ts)1325 3381 y Fx(1)1360 3373 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5536
Fw([)p Fk(as)7 b Fw(;)13 b Fk(xs)7 b Fw(]\))17 b Fm(^)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5537
b Fn(:)13 b(:)g(:)39 b Fm(^)17 b Fw(\()p Fm(8)p Fn(C)q(:P)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5538
b(C)18 b Fk(ts)2277 3381 y Fi(n)2319 3373 y Fw([)p Fk(as)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5539
b Fw(;)14 b Fk(xs)6 b Fw(]\))22 b Fm(^)1029 3477 y Fn(S)t
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5540
Fk(ss)1149 3485 y Fx(1)1183 3477 y Fw([)p Fk(as)7 b Fw(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5541
b Fk(xs)7 b Fw(])39 b Fm(^)g Fn(:)13 b(:)g(:)39 b Fm(^)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5542
Fn(S)t Fk(ss)1875 3485 y Fi(n)1918 3477 y Fw([)p Fk(as)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5543
b Fw(;)13 b Fk(xs)7 b Fw(])38 b Fm(^)p .80 .80 .80 TeXcolorrgb
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5544
.80 .80 .80 TeXcolorrgb 2272 3516 294 117 v .80 .80 .80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5545
TeXcolorrgb Black 64 w Fk(as)28 b Fw(#)21 b Fn(C)p .80 .80 .80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5546
TeXcolorrgb Black 73 w Fm(\))g Fn(P)i(C)18 b Fk(ts)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5547
b Fw([)p Fk(as)g Fw(;)13 b Fk(xs)7 b Fw(])651 3533 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5548
Fn(:)13 b(:)g(:)p 639 3580 2514 4 v 1665 3648 a(R)g Fk(ts)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5549
b Fm(\))21 b Fn(P)j(C)18 b Fk(ts)1148 b Fw(\(12\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5550
3826 y Fz(can)33 b(b)r(e)h(used,)f(where)g Fr(C)40 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5551
Fz(stands)33 b(for)f(an)h Fs(induction)j(c)l(ontext)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5552
Fz(.)c(This)i(induction)f(con)n(text)523 3926 y(can)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5553
b(b)r(e)i(instan)n(tiated)e(appropriately)f(\(w)n(e)i(will)g(explain)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5554
(this)g(in)g(the)g(next)g(section\).)g(The)523 4026 y(only)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5555
(requiremen)n(t)g(w)n(e)g(ha)n(v)n(e)f(ab)r(out)i Fr(C)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5556
b Fz(is)25 b(that)h(it)g(needs)f(to)h(b)r(e)g(\014nitely)g(supp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5557
(orted.)f(The)523 4125 y(main)h(di\013erence)g(b)r(et)n(w)n(een)g(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5558
(stronger)e(induction)i(principle)g(in)g(\(12\))g(and)g(the)g(w)n(eak)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5559
(er)523 4225 y(one)36 b(in)g(\(11\))g(is)g(that)g(in)h(a)f(pro)r(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5560
(using)h(the)g(stronger)f(w)n(e)h(can)f(assume)h(that)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5561
Fs(as)7 b Fz(,)523 4325 y(i.e.)37 b(the)g(v)-5 b(ariables)35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5562
b(in)h(binding-p)r(osition,)h(are)e(fresh)h(with)h(resp)r(ect)f(to)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5563
(the)g(con)n(text)f Fr(C)523 4424 y Fz(\(see)g(highligh)n(ted)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5564
(freshness-condition\).)g(This)h(additional)f(assumption)h(allo)n(ws)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5565
(us)i(to)523 4524 y(reason)25 b(as)g(in)i(informal)e(\\pap)r(er-and-p)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5566
(encil")f(pro)r(ofs)i(where)f(one)h(assumes)f(the)i(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5567
b(ariable)523 4623 y(con)n(v)n(en)n(tion)26 b(\(w)n(e)i(will)f(also)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5568
(sho)n(w)g(this)h(in)f(the)h(next)g(section\).)648 4725
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5569
y(The)33 b(\014rst)g(condition)h(of)f(v)n(c-compatibilit)n(y)g(implies)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5570
g(that)h(the)g(inductiv)n(ely)g(de\014ned)523 4825 y(predicate)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5571
b Fr(R)i Fz(is)f(equiv)-5 b(arian)n(t)24 b(and)i(that)g(ev)n(ery)f(sc)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5572
(hematic)g(subterm)g(o)r(ccurring)g(in)h(a)f(rule)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5573
4924 y(is)j(equiv)-5 b(arian)n(t.)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5574
%%Page: 10 10
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5575
TeXDict begin 10 9 bop Black 523 232 a Fw(10)199 b(Christian)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5576
b(Urban,)e(Stefan)h(Berghofer,)i(and)d(Mic)n(hael)i(Norrish)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5577
Black Black 523 448 a Ft(Lemma)j(3.)p Black 40 w Fs(\(a\))40
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5578
b(If)f(al)t(l)h(functions)f(in)g(a)h(schematic)g(term)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5579
Fr(t)p Fz([)p Fs(as)7 b Fz(;)14 b Fs(xs)6 b Fz(])39 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5580
Fs(ar)l(e)h(e)l(quivariant,)523 548 y(then)32 b(\(viewe)l(d)h(as)g(a)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5581
(function\))g Fr(t)g Fs(is)h(e)l(quivariant,)g(that)f(is)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5582
Fr(\031)2480 557 y Fg(\001)2532 548 y Fr(t)p Fz([)p Fs(as)8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5583
b Fz(;)14 b Fs(xs)6 b Fz(])27 b(=)g Fr(t)p Fz([)p Fr(\031)3030
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5584
557 y Fg(\001)3069 548 y Fs(as)7 b Fz(;)14 b Fr(\031)3239
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5585
557 y Fg(\001)3277 548 y Fs(xs)6 b Fz(])p Fs(.)523 648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5586
y(\(b\))27 b(If)g(al)t(l)h(functions)f(and)g(side-c)l(onditions)i(in)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5587
(the)g(rules)f(of)i(an)f(inductive)h(de\014nition)f(for)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5588
747 y(the)j(pr)l(e)l(dic)l(ate)h Fr(R)f Fs(ar)l(e)g(e)l(quivariant,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5589
(then)f Fr(R)g Fs(is)g(e)l(quivariant,)h(that)f(is)g(if)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5590
Fr(R)15 b Fs(ts)36 b(holds)31 b(than)523 847 y(also)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5591
Fr(R)14 b Fz(\()p Fr(\031)852 856 y Fg(\001)891 847 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5592
Fs(ts)6 b Fz(\))30 b Fs(holds.)p Black 523 1026 a(Pr)l(o)l(of.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5593
Black 43 w Fz(The)c(\014rst)f(part)g(is)g(b)n(y)g(a)g(routine)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5594
(induction)h(on)f(the)h(structure)f(of)g(the)h(sc)n(hematic)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5595
1125 y(term)j Fr(t)p Fz(.)f(The)h(second)f(part)g(is)g(b)n(y)g(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5596
(simple)h(rule)f(induction)h(using)f(the)h(w)n(eak)f(induction)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5597
1225 y(principle)g(giv)n(en)e(in)i(\(11\).)523 1404 y(W)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5598
b(e)31 b(no)n(w)f(pro)n(v)n(e)e(our)i(main)g(theorem:)g(if)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5599
(rules)f(of)g(an)g(inductiv)n(e)h(de\014nition)f(are)g(v)n(c-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5600
1503 y(compatible,)d(then)i(the)f(strong)e(induction)i(principle)f(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5601
(\(12\))g(holds.)p Black 523 1683 a Ft(Theorem)i(1.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5602
Black 41 w Fs(Given)42 b(an)f(inductive)h(de\014nition)g(for)g(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5603
(pr)l(e)l(dic)l(ate)h Fr(R)g Fs(involving)h(vc-)523 1783
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5604
y(c)l(omp)l(atible)38 b(schematic)f(rules)g(only,)g(then)f(a)h(str)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5605
(ong)f(induction)g(principle)j(is)d(available)523 1883
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5606
y(for)c(this)g(de\014nition)f(establishing)i(the)f(implic)l(ation)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5607
Fr(R)14 b Fs(ts)32 b Fp(\))26 b Fr(P)g(C)20 b Fs(ts)37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5608
b(with)32 b(the)f(induction)523 1982 y(c)l(ontext)e Fr(C)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5609
b Fs(b)l(eing)30 b(\014nitely)g(supp)l(orte)l(d.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5610
523 2153 a(Pr)l(o)l(of.)p Black 43 w Fz(W)-7 b(e)33 b(need)f(to)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5611
(establish)g Fr(R)15 b Fs(ts)37 b Fp(\))31 b Fr(P)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5612
b(C)20 b Fs(ts)39 b Fz(using)32 b(the)g(implications)g(indicated)h(in)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5613
523 2244 y(\(12\).)c(T)-7 b(o)30 b(do)f(so)g(w)n(e)h(will)g(use)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5614
(w)n(eak)f(induction)h(from)f(\(11\))h(and)f(establish)h(that)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5615
2335 y(prop)r(osition)d Fr(R)14 b Fs(ts)30 b Fp(\))23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5616
b(8)p Fr(\031)16 b(C)q(:P)26 b(C)20 b Fz(\()p Fr(\031)1668
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5617
2344 y Fg(\001)1707 2335 y Fs(ts)6 b Fz(\))28 b(holds.)g(F)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5618
b(or)27 b(eac)n(h)g(sc)n(hematic)g(rule)g Fr(\045)p Fz([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5619
Fs(as)7 b Fz(;)14 b Fs(xs)6 b Fz(])880 2503 y Fn(R)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5620
b Fk(ts)1014 2511 y Fx(1)1049 2503 y Fw([)p Fk(as)7 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5621
Fw(;)13 b Fk(xs)7 b Fw(])34 b Fn(:)13 b(:)h(:)34 b(R)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5622
b Fk(ts)1567 2511 y Fi(n)1610 2503 y Fw([)p Fk(as)7 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5623
Fw(;)13 b Fk(xs)7 b Fw(])77 b Fn(S)1960 2511 y Fx(1)2007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5624
2503 y Fk(ss)2076 2511 y Fx(1)2111 2503 y Fw([)p Fk(as)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5625
b Fw(;)13 b Fk(xs)7 b Fw(])34 b Fn(:)13 b(:)g(:)35 b(S)2542
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5626
2511 y Fi(m)2613 2503 y Fk(ss)2682 2511 y Fi(m)2741 2503
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5627
y Fw([)p Fk(as)7 b Fw(;)13 b Fk(xs)7 b Fw(])p 868 2550
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5628
2111 4 v 1743 2622 a Fn(R)14 b Fk(ts)6 b Fw([)p Fk(as)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5629
Fw(;)14 b Fk(xs)6 b Fw(])3020 2558 y Fn(\045)523 2789
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5630
y Fz(in)28 b(the)g(inductiv)n(e)g(de\014nition)g(w)n(e)f(ha)n(v)n(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5631
(to)h(analyse)e(one)h(case.)g(The)h(reasoning)e(pro)r(ceeds)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5632
2880 y(in)g(eac)n(h)e(of)i(them)g(as)f(follo)n(ws:)f(By)h(induction)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5633
(h)n(yp)r(othesis)f(and)h(side-conditions)e(w)n(e)h(ha)n(v)n(e)1005
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5634
3045 y Fw(\()p Fm(8)p Fn(\031)15 b(C)q(:P)24 b(C)18 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5635
Fw(\()p Fn(\031)1437 3054 y Fg(\001)1474 3045 y Fk(ts)1537
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5636
3053 y Fx(1)1572 3045 y Fw([)p Fk(as)7 b Fw(;)13 b Fk(xs)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5637
b Fw(]\)\))34 b Fn(:)13 b(:)g(:)35 b Fw(\()p Fm(8)p Fn(\031)15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5638
b(C)q(:P)23 b(C)18 b Fw(\()p Fn(\031)2447 3054 y Fg(\001)2485
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5639
3045 y Fk(ts)2548 3053 y Fi(n)2590 3045 y Fw([)p Fk(as)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5640
b Fw(;)14 b Fk(xs)6 b Fw(]\)\))p Black 392 w(\(13\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5641
Black 1350 3161 a Fn(S)1397 3169 y Fx(1)1444 3161 y Fk(ss)1513
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5642
3169 y Fx(1)1548 3161 y Fw([)p Fk(as)h Fw(;)13 b Fk(xs)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5643
b Fw(])34 b Fn(:)13 b(:)g(:)35 b(S)1979 3169 y Fi(m)2050
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5644
3161 y Fk(ss)2119 3169 y Fi(m)2178 3161 y Fw([)p Fk(as)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5645
b Fw(;)13 b Fk(xs)7 b Fw(])p Black 864 w(\(14\))p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5646
523 3328 a Fz(hold.)43 b(Since)f Fr(\045)h Fz(is)f(assumed)g(to)h(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5647
(e)g(v)n(c-compatible,)e(w)n(e)h(ha)n(v)n(e)g(b)n(y)g(Lem.)h(3)f(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5648
(\(*\))523 3419 y Fr(\031)573 3428 y Fg(\001)612 3419
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5649
y Fs(ts)680 3431 y Fq(i)708 3419 y Fz([)p Fs(as)7 b Fz(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5650
b Fs(xs)6 b Fz(])39 b(is)g(equal)f(to)h Fs(ts)1499 3431
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5651
y Fq(i)1526 3419 y Fz([)p Fr(\031)1599 3428 y Fg(\001)1638
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5652
3419 y Fs(as)7 b Fz(;)14 b Fr(\031)1808 3428 y Fg(\001)1846
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5653
3419 y Fs(xs)7 b Fz(])39 b(in)g(\(13\).)g(F)-7 b(or)38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5654
b(\(14\))h(w)n(e)f(can)h(further)g(infer)523 3511 y(from)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5655
b(the)h(v)n(c-compatibilit)n(y)f(of)g Fr(\045)h Fz(that)1195
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5656
3676 y Fw(\()p Fn(a)p Fw(\))20 b Fk(as)28 b Fw(#)22 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5657
Fk(ts)7 b Fw([)p Fk(as)g Fw(;)13 b Fk(xs)7 b Fw(])154
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5658
b(and)f(\()p Fn(b)p Fw(\))21 b Fn(distinct)p Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5659
Fk(as)6 b Fw(\))535 b(\(15\))523 3850 y Fz(hold.)27 b(W)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5660
b(e)27 b(ha)n(v)n(e)e(to)i(sho)n(w)e(that)i Fr(P)f(C)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5661
b Fz(\()p Fr(\031)1786 3859 y Fg(\001)1825 3850 y Fs(ts)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5662
b Fz([)p Fs(as)h Fz(;)14 b Fs(xs)6 b Fz(]\))28 b(holds,)e(whic)n(h)g(b)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5663
r(ecause)h(of)f(Lem.)h(3)f(is)523 3950 y(equiv)-5 b(alen)n(t)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5664
b(to)h Fr(P)e(C)20 b Fs(ts)6 b Fz([)p Fr(\031)1318 3959
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5665
y Fg(\001)1357 3950 y Fs(as)h Fz(;)14 b Fr(\031)1527
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5666
3959 y Fg(\001)1565 3950 y Fs(xs)6 b Fz(].)523 4095 y(The)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5667
b(pro)r(of)g(pro)r(ceeds)g(b)n(y)g(using)g(Lem.)g(2)g(and)h(c)n(ho)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5668
(osing)e(for)h(ev)n(ery)f(atom)h Fr(a)g Fz(in)h Fs(as)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5669
b Fz(a)25 b(fresh)523 4186 y(atom)i Fr(c)h Fz(suc)n(h)f(that)h(for)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5670
(all)g(the)h Fs(cs)35 b Fz(the)28 b(follo)n(wing)e(holds:)693
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5671
4351 y Fw(\()p Fn(a)p Fw(\))21 b Fk(cs)28 b Fw(#)21 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5672
Fk(ts)7 b Fw([)p Fn(\031)1125 4360 y Fg(\001)1163 4351
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5673
y Fk(as)g Fw(;)13 b Fn(\031)1321 4360 y Fg(\001)1359
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5674
4351 y Fk(xs)7 b Fw(])107 b(\()p Fn(b)p Fw(\))21 b Fk(cs)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5675
b Fw(#)21 b Fn(\031)1900 4360 y Fg(\001)1938 4351 y Fk(as)113
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5676
b Fw(\()p Fn(c)p Fw(\))22 b Fk(cs)28 b Fw(#)21 b Fn(C)112
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5677
b Fw(\()p Fn(d)p Fw(\))21 b Fn(distinct)p Fw(\()p Fk(cs)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5678
b Fw(\))170 b(\(16\))523 4526 y Fz(Suc)n(h)31 b Fs(cs)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5679
b Fz(alw)n(a)n(ys)29 b(exists:)i(the)h(\014rst)f(and)g(the)h(second)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5680
(prop)r(ert)n(y)h(can)f(b)r(e)i(obtained)f(since)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5681
4625 y(the)23 b(sc)n(hematic)e(terms)h Fs(ts)6 b Fz([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5682
Fr(\031)1403 4634 y Fg(\001)1442 4625 y Fs(as)h Fz(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5683
b Fr(\031)1612 4634 y Fg(\001)1650 4625 y Fs(xs)7 b Fz(])22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5684
b(and)g Fr(\031)1981 4634 y Fg(\001)2019 4625 y Fs(as)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5685
b Fz(stand)22 b(for)g(\014nitely)h(supp)r(orted)e(ob)5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5686
b(jects;)523 4725 y(the)25 b(third)h(can)e(also)g(b)r(e)i(obtained)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5687
(since)h(w)n(e)g(assumed)f(that)h(the)h(induction)f(con)n(text)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5688
Fr(C)31 b Fz(is)523 4825 y(\014nitely)25 b(supp)r(orted;)f(the)g(last)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5689
(can)g(b)r(e)g(obtained)g(b)n(y)g(c)n(ho)r(osing)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5690
Fs(cs)31 b Fz(one)24 b(after)g(another)523 4924 y(a)n(v)n(oiding)i(the)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5691
i(ones)f(that)h(ha)n(v)n(e)e(already)g(b)r(een)i(c)n(hosen.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5692
Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5693
%%Page: 11 11
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5694
TeXDict begin 11 10 bop Black 1347 232 a Fw(Barendregt's)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5695
b(V)-6 b(ariable)26 b(Con)n(v)n(en)n(tion)f(in)h(Rule)f(Inductions)198
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5696
b(11)p Black 648 461 a Fz(No)n(w)19 b(w)n(e)h(form)f(the)i(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5697
(utation)e Fr(\031)1785 431 y Fj(0)1832 414 y Fy(def)1843
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5698
461 y Fz(=)34 b(\()p Fr(\031)2024 470 y Fg(\001)2063
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5699
461 y Fs(as)44 b(cs)7 b Fz(\))20 b(where)f(\()p Fr(\031)2628
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5700
470 y Fg(\001)2667 461 y Fs(as)44 b(cs)7 b Fz(\))21 b(stands)e(for)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5701
(the)523 552 y(sequence)29 b(of)h(sw)n(appings)f(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5702
Fr(\031)1446 561 y Fg(\001)1484 552 y Fr(a)1528 564 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5703
Fy(1)1606 552 y Fr(c)1642 564 y Fy(1)1679 552 y Fz(\))14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5704
b Fr(:)g(:)g(:)g Fz(\()p Fr(\031)1918 561 y Fg(\001)1957
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5705
552 y Fr(a)2001 564 y Fq(j)2076 552 y Fr(c)2112 564 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5706
Fq(j)2147 552 y Fz(\).)31 b(Since)f(p)r(erm)n(utations)f(are)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5707
(bijectiv)n(e)523 644 y(renamings,)24 b(w)n(e)i(can)f(infer)g(from)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5708
(\(15.)p Fr(b)p Fz(\))f(that)h Fs(distinct)8 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5709
Fr(\031)2363 653 y Fg(\001)2402 644 y Fs(as)f Fz(\))26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5710
b(holds.)f(This)g(and)h(the)g(fact)523 735 y(in)i(\(16.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5711
Fr(d)p Fz(\))f(implies)h(that)1516 826 y Fn(\031)1563
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5712
790 y Fl(0)1585 826 y Fw(@)p Fn(\031)1692 835 y Fg(\001)1729
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5713
826 y Fk(as)g Fw(=)22 b Fn(\031)1956 790 y Fl(0)1978
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5714
835 y Fg(\001)2016 826 y Fw(\()p Fn(\031)2093 835 y Fg(\001)2130
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5715
826 y Fk(as)7 b Fw(\))21 b(=)g Fk(cs)863 b Fw(\(17\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5716
947 y Fz(W)-7 b(e)29 b(then)h(instan)n(tiate)e(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5717
Fr(\031)i Fz(in)d(the)h(induction)f(h)n(yp)r(otheses)f(giv)n(en)g(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5718
(\(13\))g(with)g Fr(\031)3266 917 y Fj(0)3290 947 y Fz(@)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5719
Fr(\031)523 1039 y Fz(and)e(obtain)h(using)f(\(17\))g(and)h(\(*\))f(so)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5720
g(that)993 1194 y Fw(\()p Fm(8)p Fn(C)q(:P)c(C)18 b Fk(ts)1351
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5721
1202 y Fx(1)1385 1194 y Fw([)p Fk(cs)8 b Fw(;)13 b Fn(\031)1561
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5722
1158 y Fl(0)1583 1194 y Fw(@)p Fn(\031)1690 1203 y Fg(\001)1727
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5723
1194 y Fk(xs)7 b Fw(]\)\))34 b Fn(:)13 b(:)g(:)35 b Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5724
Fm(8)p Fn(C)q(:P)23 b(C)18 b Fk(ts)2397 1202 y Fi(n)2440
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5725
1194 y Fw([)p Fk(cs)7 b Fw(;)13 b Fn(\031)2615 1158 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5726
Fl(0)2637 1194 y Fw(@)p Fn(\031)2744 1203 y Fg(\001)2781
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5727
1194 y Fk(xs)7 b Fw(]\)\))333 b(\(18\))523 1349 y Fz(hold.)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5728
b(Since)f(the)h(rule)f Fr(\045)h Fz(is)f(v)n(c-compatible,)g(w)n(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5729
(can)g(infer)g(from)h(\(14\))f(and)g(the)h(equiv)-5 b(ari-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5730
1440 y(ance)27 b(of)h(the)g(side-conditions)e(that)1227
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5731
1595 y Fn(S)1274 1603 y Fx(1)1322 1595 y Fk(ss)1390 1603
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5732
y Fx(1)1425 1595 y Fw([)p Fk(cs)7 b Fw(;)13 b Fn(\031)1600
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5733
1559 y Fl(0)1622 1595 y Fw(@)p Fn(\031)1729 1604 y Fg(\001)1767
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5734
1595 y Fk(xs)7 b Fw(])34 b Fn(:)13 b(:)g(:)35 b(S)2066
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5735
1603 y Fi(m)2137 1595 y Fk(ss)2206 1603 y Fi(m)2265 1595
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5736
y Fw([)p Fk(cs)7 b Fw(;)13 b Fn(\031)2440 1559 y Fl(0)2462
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5737
1595 y Fw(@)p Fn(\031)2569 1604 y Fg(\001)2606 1595 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5738
Fk(xs)7 b Fw(])568 b(\(19\))523 1750 y Fz(hold)31 b(\(w)n(e)g(use)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5739
(here)h(the)g(fact)g(that)g Fr(\031)1745 1720 y Fj(0)1769
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5740
1750 y Fz(@)p Fr(\031)1884 1759 y Fg(\001)1922 1750 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5741
Fz(\()p Fs(ss)2029 1762 y Fq(i)2057 1750 y Fz([)p Fs(as)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5742
b Fz(;)14 b Fs(xs)6 b Fz(]\))31 b(is)g(equal)g(to)f Fs(ss)2854
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5743
1762 y Fq(i)2882 1750 y Fz([)p Fs(cs)7 b Fz(;)14 b Fr(\031)3071
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5744
1720 y Fj(0)3094 1750 y Fz(@)p Fr(\031)3209 1759 y Fg(\001)3247
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5745
1750 y Fs(xs)7 b Fz(]\).)523 1841 y(F)-7 b(rom)29 b(\(16.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5746
Fr(c)p Fz(\),)g(\(18\),)g(\(19\))g(and)g(the)h(implication)f(from)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5747
(the)g(strong)f(induction)i(principle)523 1933 y(w)n(e)d(can)g(infer)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5748
Fr(P)35 b(C)29 b Fs(ts)7 b Fz([)p Fs(cs)g Fz(;)14 b Fr(\031)1423
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5749
1902 y Fj(0)1446 1933 y Fz(@)p Fr(\031)1561 1942 y Fg(\001)1599
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5750
1933 y Fs(xs)7 b Fz(])27 b(whic)n(h)h(b)n(y)f(Lem.)h(3)f(is)g(equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5751
b(alen)n(t)28 b(to)1600 2088 y Fn(P)k(C)26 b(\031)1809
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5752
2052 y Fl(0)1831 2097 y Fg(\001)1869 2088 y Fk(ts)7 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5753
Fw([)p Fn(\031)2000 2097 y Fg(\001)2038 2088 y Fk(as)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5754
Fw(;)13 b Fn(\031)2196 2097 y Fg(\001)2234 2088 y Fk(xs)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5755
b Fw(])940 b(\(20\))523 2243 y Fz(F)-7 b(rom)32 b(\(15.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5756
Fr(a)p Fz(\))g(w)n(e)g(can)f(b)n(y)h(Lem.)h(1\()p Fr(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5757
Fz(\))f(infer)g(that)h Fr(\031)2223 2252 y Fg(\001)2261
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5758
2243 y Fs(as)38 b Fz(#)31 b Fs(ts)6 b Fz([)p Fr(\031)2616
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5759
2252 y Fg(\001)2655 2243 y Fs(as)h Fz(;)14 b Fr(\031)2825
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5760
2252 y Fg(\001)2863 2243 y Fs(xs)7 b Fz(])32 b(holds.)g(This)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5761
2334 y(ho)n(w)n(ev)n(er)26 b(implies)h(b)n(y)h(\(16.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5762
Fr(a)p Fz(\))f(and)g(b)n(y)h(rep)r(eated)f(application)g(of)g(Lem.)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5763
(1\()p Fr(b)p Fz(\))f(that)1400 2489 y Fn(\031)1447 2453
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5764
y Fl(0)1469 2498 y Fg(\001)1508 2489 y Fk(ts)6 b Fw([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5765
Fn(\031)1638 2498 y Fg(\001)1677 2489 y Fk(as)g Fw(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5766
b Fn(\031)1834 2498 y Fg(\001)1872 2489 y Fk(xs)7 b Fw(])22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5767
b(=)f Fk(ts)7 b Fw([)p Fn(\031)2200 2498 y Fg(\001)2238
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5768
2489 y Fk(as)g Fw(;)13 b Fn(\031)2396 2498 y Fg(\001)2433
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5769
2489 y Fk(xs)7 b Fw(])741 b(\(21\))523 2652 y Fz(Substituting)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5770
b(this)f(equation)g(in)n(to)g(\(20\))f(establishes)h(the)g(pro)r(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5771
(obligation)e(for)i(the)g(rule)523 2752 y Fr(\045)p Fz(.)h(Pro)n(vided)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5772
e(w)n(e)i(analysed)e(all)i(suc)n(h)g(cases,)e(w)n(e)i(ha)n(v)n(e)f(sho)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5773
n(wn)g Fr(R)14 b Fs(ts)30 b Fp(\))24 b(8)p Fr(\031)16
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5774
b(C)q(:P)26 b(C)20 b Fz(\()p Fr(\031)3242 2761 y Fg(\001)3281
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5775
2752 y Fs(ts)7 b Fz(\).)523 2851 y(W)-7 b(e)22 b(obtain)e(our)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5776
(original)e(goal)h(b)n(y)h(instan)n(tiating)g Fr(\031)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5777
Fz(with)e(the)g(iden)n(tit)n(y)f(p)r(erm)n(utation.)83
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5778
b Fp(u)-55 b(t)523 3110 y Fu(5)112 b(Examples)523 3302
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5779
y Fz(W)-7 b(e)28 b(can)f(no)n(w)g(apply)h(our)e(tec)n(hnique)i(to)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5780
(the)h(examples)f(from)h(the)g(In)n(tro)r(duction.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5781
3545 y Ft(5.1)95 b(Simple)29 b(T)m(yping)523 3704 y Fz(Giv)n(en)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5782
b(the)h(t)n(yping)f(relation)g(de\014ned)h(in)f(\(2\))q(,)g(w)n(e)g(m)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5783
(ust)h(\014rst)f(c)n(hec)n(k)g(the)h(conditions)f(sp)r(elt)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5784
3803 y(out)34 b(in)g(De\014nition)h(5.)e(The)h(\014rst)g(condition)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5785
(is)h(that)g(all)g(of)f(the)i(de\014nition's)f(functions)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5786
3903 y(\(namely)23 b Fs(var)10 b Fz(,)24 b Fs(app)6 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5787
Fz(,)24 b Fr(l)r(am)f Fz(and)g(::\))h(and)f(side-conditions)g(\(namely)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5788
g Fs(valid)r Fz(,)h Fp(2)g Fz(and)f(#\))h(m)n(ust)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5789
4003 y(b)r(e)33 b(equiv)-5 b(arian)n(t.)31 b(This)h(is)g(easily)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5790
(con\014rmed)h(\(see)g(Remark)f(1\).)h(The)h(second)e(condition)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5791
4102 y(requires)25 b(that)i(all)g(v)-5 b(ariables)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5792
b(in)i(binding)g(p)r(ositions)f(b)r(e)h(distinct)h(\(there)e(is)h(just)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5793
g(one,)g(the)523 4202 y Fr(x)k Fz(in)g(T)n(yp)r(e)888
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5794
4214 y Fy(3)925 4202 y Fz(\);)h(and)e(that)h(it)h(b)r(e)f(fresh)f(for)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5795
(all)f(the)h(terms)g(app)r(earing)f(in)h(the)g(conclusion)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5796
4301 y(of)h(that)f(rule,)h(namely)f Fr(\000)41 b Fp(`)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5797
b Fs(lam)7 b Fz(\()p Fr(x:M)i Fz(\))30 b(:)g Fr(T)1957
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5798
4313 y Fy(1)2023 4301 y Fp(!)g Fr(T)2185 4313 y Fy(2)2222
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5799
4301 y Fz(,)i(under)f(the)h(assumption)f(that)h(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5800
4401 y(side-condition,)27 b Fr(x)c Fz(#)h Fr(\000)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5801
b Fz(,)27 b(of)h(this)g(rule)f(holds.)648 4501 y(In)41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5802
b(this)g(case,)g(therefore,)f(w)n(e)h(m)n(ust)g(c)n(hec)n(k)g(that)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5803
Fr(x)46 b Fz(#)g Fr(\000)12 b Fz(,)41 b Fr(x)46 b Fz(#)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5804
Fs(lam)7 b Fz(\()p Fr(x:M)i Fz(\))42 b(and)523 4600 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5805
Fr(x)c Fz(#)f Fr(T)763 4612 y Fy(1)837 4600 y Fp(!)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5806
Fr(T)1006 4612 y Fy(2)1079 4600 y Fz(hold.)f(The)h(\014rst)e(is)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5807
(immediate)h(giv)n(en)e(our)g(assumption;)h(the)h(second)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5808
4700 y(follo)n(ws)24 b(from)h(the)g(de\014nition)g(of)g(supp)r(ort)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5809
(for)f(lam)n(b)r(da-terms)g(\()p Fr(x)g Fz(#)f Fs(lam)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5810
b Fz(\()p Fr(x:M)i Fz(\))25 b(for)g(all)f Fr(x)523 4800
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5811
y Fz(and)f Fr(M)9 b Fz(\);)23 b(and)h(the)f(third)h(follo)n(ws)e(from)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5812
(the)h(de\014nition)f(of)g(supp)r(ort)h(for)e(t)n(yp)r(es)i(\(w)n(e)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5813
(de\014ne)523 4924 y(p)r(erm)n(utation)k(on)h(t)n(yp)r(es)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5814
Fr(T)39 b Fz(as)27 b Fr(\031)1573 4933 y Fg(\001)1611
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5815
4924 y Fr(T)1694 4877 y Fy(def)1706 4924 y Fz(=)33 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5816
Fr(T)39 b Fz(and)27 b(th)n(us)h(obtain)f(that)h Fe(supp)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5817
Fz(\()p Fr(T)12 b Fz(\))22 b(=)h Fh(?)p Fz(\).)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5818
Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5819
%%Page: 12 12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5820
TeXDict begin 12 11 bop Black 523 232 a Fw(12)199 b(Christian)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5821
b(Urban,)e(Stefan)h(Berghofer,)i(and)d(Mic)n(hael)i(Norrish)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5822
Black 648 448 a Fz(With)38 b(these)f(conditions)g(established,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5823
(Theorem)g(1)g(tells)h(us)f(that)h(the)g(strong,)e(or)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5824
540 y(v)n(c-compatible)26 b(principle)i(exists,)f(and)h(that)g(it)g(is)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5825
772 688 y Fm(8)p Fn(\000)c(x)12 b(T)23 b(C)q(:)f(v)s(al)q(id)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5826
Fw(\()p Fn(\000)11 b Fw(\))16 b Fm(^)h Fw(\()p Fn(x)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5827
Fw(:)h Fn(T)11 b Fw(\))20 b Fm(2)i Fn(\000)32 b Fm(\))21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5828
b Fn(P)32 b(C)26 b(\000)32 b Fw(\()p Fk(var)9 b Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5829
Fn(x)p Fw(\)\))20 b Fn(T)772 803 y Fm(8)p Fn(\000)k(M)d(N)g(T)1108
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5830
811 y Fx(1)1155 803 y Fn(T)1200 811 y Fx(2)1247 803 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5831
Fn(C)q(:)33 b Fw(\()p Fm(8)p Fn(C)q(:)43 b(P)32 b(C)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5832
b(\000)32 b(M)e Fw(\()p Fn(T)1970 811 y Fx(1)2025 803
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5833
y Fm(!)21 b Fn(T)2168 811 y Fx(2)2203 803 y Fw(\)\))38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5834
b Fm(^)h Fw(\()p Fm(8)p Fn(C)q(:)j(P)32 b(C)26 b(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5835
b(N)e(T)2960 811 y Fx(1)2995 803 y Fw(\))42 b Fm(\))1357
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5836
894 y Fn(P)32 b(C)27 b(\000)32 b Fw(\()p Fk(app)5 b Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5837
Fn(M)t(;)13 b(N)8 b Fw(\)\))21 b Fn(T)2088 902 y Fx(2)772
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5838
985 y Fm(8)p Fn(\000)j(x)12 b(M)21 b(T)1082 993 y Fx(1)1129
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5839
985 y Fn(T)1174 993 y Fx(2)1221 985 y Fn(C)q(:)33 b(x)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5840
b Fw(#)h Fn(\000)49 b Fm(^)38 b Fw(\()p Fm(8)p Fn(C)q(:)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5841
b(P)32 b(C)27 b Fw(\(\()p Fn(x)20 b Fw(:)i Fn(T)2213
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5842
993 y Fx(1)2247 985 y Fw(\))9 b(::)g Fn(\000)i Fw(\))21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5843
b Fn(M)29 b(T)2594 993 y Fx(2)2629 985 y Fw(\))38 b Fm(^)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5844
Fn(x)20 b Fw(#)i Fn(C)48 b Fm(\))1331 1077 y Fn(P)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5845
b(C)27 b(\000)32 b Fw(\()p Fk(lam)5 b Fw(\()p Fn(x:M)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5846
Fw(\)\))21 b(\()p Fn(T)2063 1085 y Fx(1)2119 1077 y Fm(!)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5847
Fn(T)2262 1085 y Fx(2)2296 1077 y Fw(\))p 772 1124 2383
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5848
4 v 1508 1192 a Fn(\000)32 b Fm(`)21 b Fn(M)30 b Fw(:)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5849
b Fn(T)53 b Fm(\))42 b Fn(P)32 b(C)27 b(\000)32 b(M)d(T)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5850
1344 y Fz(This)24 b(principle)g(can)f(no)n(w)g(b)r(e)h(used)g(to)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5851
(establish)f(the)h(w)n(eak)n(ening)f(result.)g(The)h(statemen)n(t)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5852
1435 y(is)1089 1526 y Fn(\000)32 b Fm(`)21 b Fn(M)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5853
b Fw(:)22 b Fn(T)53 b Fm(\))43 b Fn(\000)32 b Fm(\022)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5854
b Fn(\000)1818 1490 y Fl(0)1882 1526 y Fm(\))43 b Fk(valid)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5855
b Fw(\()p Fn(\000)2254 1490 y Fl(0)2276 1526 y Fw(\))43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5856
b Fm(\))f Fn(\000)2526 1490 y Fl(0)2569 1526 y Fm(`)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5857
b Fn(M)29 b Fw(:)22 b Fn(T)439 b Fw(\(22\))523 1645 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5858
Fz(With)25 b(the)g(strong)d(induction)j(principle,)f(the)g(formal)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5859
(pro)r(of)f(of)h(this)h(statemen)n(t)f(pro)r(ceeds)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5860
1737 y(lik)n(e)35 b(the)g(informal)f(one)h(giv)n(en)f(in)h(the)g(In)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5861
(tro)r(duction.)g(There,)f(in)h(the)g(T)n(yp)r(e)3032
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5862
1749 y Fy(3)3104 1737 y Fz(case,)f(w)n(e)523 1828 y(used)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5863
b(the)f(v)-5 b(ariable)23 b(con)n(v)n(en)n(tion)f(to)h(assume)g(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5864
(the)g(b)r(ound)g Fr(x)g Fz(w)n(as)e(fresh)i(for)f Fr(\000)3123
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5865
1798 y Fj(0)3146 1828 y Fz(.)g(Giv)n(en)523 1919 y(this)j(information,)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5866
f(w)n(e)g(instan)n(tiate)g(the)g(induction)h(con)n(text)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5867
Fr(C)32 b Fz(in)26 b(the)f(strong)g(induction)523 2011
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5868
y(principle)d(with)h Fr(\000)1106 1980 y Fj(0)1151 2011
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5869
y Fz(\(whic)n(h)g(is)f(\014nitely)h(supp)r(orted\).)f(The)g(complete)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5870
(instan)n(tiation)e(of)i(the)523 2102 y(v)n(c-compatible)j(induction)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5871
(principle)g(is)1095 2250 y Fn(P)k Fw(=)21 b Fn(\025\000)i(M)e(T)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5872
(\000)1593 2218 y Fl(0)1615 2250 y Fn(:)43 b(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5873
b Fm(\022)21 b Fn(\000)1897 2218 y Fl(0)1940 2250 y Fm(\))g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5874
Fk(valid)8 b Fw(\()p Fn(\000)2291 2218 y Fl(0)2313 2250
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5875
y Fw(\))21 b Fm(\))g Fn(\000)2520 2218 y Fl(0)2563 2250
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5876
y Fm(`)h Fn(M)29 b Fw(:)22 b Fn(T)1033 2341 y(C)27 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5877
Fw(=)21 b Fn(\000)1254 2310 y Fl(0)1583 2341 y Fn(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5878
b Fw(=)21 b Fn(\000)317 b(M)30 b Fw(=)21 b Fn(M)316 b(T)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5879
b Fw(=)21 b Fn(T)523 2499 y Fz(whic)n(h)h(after)g(some)f(b)r(eta-con)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5880
(tractions)f(giv)n(es)h(us)h(the)g(statemen)n(t)g(in)h(\(22\).)f(The)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5881
(induction)523 2599 y(cases)27 b(are)f(then)i(as)f(follo)n(ws)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5882
(\(stripping)g(o\013)h(the)g(outermost)f(quan)n(ti\014ers\):)632
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5883
2767 y(\(1\))48 b Fs(valid)10 b Fz(\()p Fr(\000)i Fz(\))42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5884
b Fp(^)g Fz(\()p Fr(x)23 b Fz(:)h Fr(T)12 b Fz(\))22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5885
b Fp(2)h Fr(\000)58 b Fp(\))46 b Fr(\000)35 b Fp(\022)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5886
b Fr(\000)2047 2737 y Fj(0)2116 2767 y Fp(\))46 b Fs(valid)10
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5887
b Fz(\()p Fr(\000)2518 2737 y Fj(0)2541 2767 y Fz(\))24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5888
b Fp(\))f Fr(\000)2766 2737 y Fj(0)2812 2767 y Fp(`)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5889
Fs(var)10 b Fz(\()p Fr(x)p Fz(\))24 b(:)f Fr(T)632 2914
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5890
y Fz(\(2\))48 b(\()p Fp(8)p Fr(\000)928 2884 y Fj(00)969
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5891
2914 y Fr(:)23 b(\000)35 b Fp(\022)23 b Fr(\000)1252
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5892
2884 y Fj(00)1317 2914 y Fp(\))g Fs(valid)10 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5893
Fr(\000)1696 2884 y Fj(00)1738 2914 y Fz(\))24 b Fp(\))f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5894
Fr(\000)1963 2884 y Fj(00)2028 2914 y Fp(`)g Fr(M)2183
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5895
2926 y Fy(1)2243 2914 y Fz(:)g Fr(T)2338 2926 y Fy(1)2398
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5896
2914 y Fp(!)g Fr(T)2553 2926 y Fy(2)2589 2914 y Fz(\))h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5897
Fp(^)786 3013 y Fz(\()p Fp(8)p Fr(\000)928 2983 y Fj(00)969
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5898
3013 y Fr(:)f(\000)35 b Fp(\022)23 b Fr(\000)1252 2983
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5899
y Fj(00)1317 3013 y Fp(\))g Fs(valid)10 b Fz(\()p Fr(\000)1696
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5900
2983 y Fj(00)1738 3013 y Fz(\))24 b Fp(\))f Fr(\000)1963
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5901
2983 y Fj(00)2028 3013 y Fp(`)g Fr(M)2183 3025 y Fy(2)2243
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5902
3013 y Fz(:)g Fr(T)2338 3025 y Fy(1)2375 3013 y Fz(\))46
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5903
b Fp(\))786 3113 y Fr(\000)34 b Fp(\022)23 b Fr(\000)1022
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5904
3083 y Fj(0)1091 3113 y Fp(\))46 b Fs(valid)11 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5905
Fr(\000)1494 3083 y Fj(0)1517 3113 y Fz(\))46 b Fp(\))g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5906
Fr(\000)1787 3083 y Fj(0)1833 3113 y Fp(`)23 b Fs(app)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5907
b Fz(\()p Fr(M)2153 3125 y Fy(1)2190 3113 y Fr(;)14 b(M)2308
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5908
3125 y Fy(2)2344 3113 y Fz(\))24 b(:)f Fr(T)2495 3125
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5909
y Fy(2)632 3260 y Fz(\(3\))48 b(\()p Fp(8)p Fr(\000)928
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5910
3230 y Fj(00)969 3260 y Fr(:)23 b Fz(\()p Fr(x)h Fz(:)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5911
Fr(T)1213 3272 y Fy(1)1250 3260 y Fz(\))9 b(::)g Fr(\000)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5912
b Fp(\022)22 b Fr(\000)1583 3230 y Fj(00)1671 3260 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5913
Fp(\))h Fs(valid)11 b Fz(\()p Fr(\000)2051 3230 y Fj(00)2093
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5914
3260 y Fz(\))46 b Fp(\))h Fr(\000)2364 3230 y Fj(00)2429
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5915
3260 y Fp(`)23 b Fr(M)31 b Fz(:)23 b Fr(T)2710 3272 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5916
Fy(2)2747 3260 y Fz(\))42 b Fp(^)g Fr(x)23 b Fz(#)g Fr(\000)3143
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5917
3230 y Fj(0)3213 3260 y Fp(\))786 3360 y Fr(\000)34 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5918
Fp(\022)23 b Fr(\000)1022 3329 y Fj(0)1091 3360 y Fp(\))46
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5919
b Fs(valid)11 b Fz(\()p Fr(\000)1494 3329 y Fj(0)1517
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5920
3360 y Fz(\))46 b Fp(\))g Fr(\000)1787 3329 y Fj(0)1833
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5921
3360 y Fp(`)23 b Fs(lam)7 b Fz(\()p Fr(x:M)i Fz(\))24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5922
b(:)f Fr(T)2388 3372 y Fy(1)2448 3360 y Fp(!)g Fr(T)2603
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5923
3372 y Fy(2)523 3530 y Fz(The)44 b(\014rst)f(t)n(w)n(o)h(cases)e(are)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5924
(trivial.)g(F)-7 b(or)43 b(\(3\),)h(w)n(e)g(instan)n(tiate)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5925
Fr(\000)2705 3499 y Fj(00)2791 3530 y Fz(in)h(the)h(induction)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5926
3629 y(h)n(yp)r(othesis)39 b(to)h(b)r(e)g(\()p Fr(x)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5927
Fz(:)g Fr(T)1422 3641 y Fy(1)1458 3629 y Fz(\))30 b(::)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5928
Fr(\000)1659 3599 y Fj(0)1682 3629 y Fz(.)40 b(F)-7 b(rom)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5929
b(the)h(assumption)f Fr(\000)55 b Fp(\022)43 b Fr(\000)2858
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5930
3599 y Fj(0)2921 3629 y Fz(w)n(e)c(ha)n(v)n(e)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5931
Fr(x)44 b Fz(:)523 3729 y Fr(T)572 3741 y Fy(1)609 3729
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5932
y Fz(\))18 b(::)f Fr(\000)43 b Fp(\022)31 b Fz(\()p Fr(x)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5933
Fz(:)f Fr(T)1126 3741 y Fy(1)1163 3729 y Fz(\))18 b(::)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5934
Fr(\000)1340 3699 y Fj(0)1362 3729 y Fz(.)33 b(Moreo)n(v)n(er)d(from)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5935
(the)h(assumption)f Fs(valid)10 b Fz(\()p Fr(\000)2854
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5936
3699 y Fj(0)2878 3729 y Fz(\))33 b(w)n(e)f(also)f(ha)n(v)n(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5937
3828 y Fs(valid)10 b Fz(\(\()p Fr(x)26 b Fz(:)e Fr(T)934
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5938
3840 y Fy(1)971 3828 y Fz(\))10 b(::)g Fr(\000)1132 3798
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5939
y Fj(0)1156 3828 y Fz(\))29 b(using)e(the)i(v)-5 b(ariable)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5940
b(con)n(v)n(en)n(tion's)g Fr(x)e Fz(#)f Fr(\000)2590
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5941
3798 y Fj(0)2613 3828 y Fz(.)29 b(Hence)f(w)n(e)g(can)g(deriv)n(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5942
3928 y(\()p Fr(x)d Fz(:)f Fr(T)723 3940 y Fy(1)760 3928
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5943
y Fz(\))10 b(::)g Fr(\000)921 3898 y Fj(0)970 3928 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5944
Fp(`)24 b Fr(M)33 b Fz(:)24 b Fr(T)1255 3940 y Fy(2)1320
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5945
3928 y Fz(using)k(the)h(induction)f(h)n(yp)r(othesis.)g(No)n(w)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5946
(applying)g(rule)g(T)n(yp)r(e)3368 3940 y Fy(3)523 4028
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5947
y Fz(w)n(e)i(can)g(obtain)g Fr(\000)1127 3998 y Fj(0)1177
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5948
4028 y Fp(`)d Fs(lam)7 b Fz(\()p Fr(x:M)i Fz(\))28 b(:)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5949
Fr(T)1744 4040 y Fy(1)1809 4028 y Fp(!)g Fr(T)1968 4040
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5950
y Fy(2)2005 4028 y Fz(,)j(again)f(using)h(the)h(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5951
b(ariable)29 b(con)n(v)n(en)n(tion's)523 4127 y Fr(x)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5952
b Fz(#)g Fr(\000)774 4097 y Fj(0)797 4127 y Fz(.)f(This)g(completes)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5953
(the)h(pro)r(of.)e(Its)h Fs(r)l(e)l(adable)44 b Fz(v)n(ersion)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5954
b(expressed)h(in)i(Isab)r(elle's)523 4227 y(Isar-language)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5955
b([12])j(and)h(using)f(the)h(nominal)g(datat)n(yp)r(e)f(pac)n(k)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5956
b(age)21 b([9])h(is)h(sho)n(wn)f(in)h(Fig.)f(1.)648 4327
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5957
y(By)h(w)n(a)n(y)f(of)i(con)n(trast,)e(recall)h(that)h(a)f(pro)r(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5958
(without)h(the)g(stronger)d(induction)j(princi-)523 4426
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5959
y(ple)i(w)n(ould)f(not)g(b)r(e)h(able)f(to)h(assume)f(an)n(ything)g(ab)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5960
r(out)g(the)h(relationship)f(b)r(et)n(w)n(een)g Fr(x)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5961
Fz(and)523 4526 y Fr(\000)586 4496 y Fj(0)609 4526 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5962
Fz(,)f(forcing)f(the)h(pro)n(v)n(er)d(to)j Fr(\013)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5963
Fz(-con)n(v)n(ert)e Fs(lam)7 b Fz(\()p Fr(x:M)i Fz(\))25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5964
b(to)g(a)f(form)g(with)i(a)e(new)h(and)f(suitably)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5965
4625 y(fresh)j(b)r(ound)h(v)-5 b(ariable,)26 b Fs(lam)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5966
b Fz(\()p Fr(z)t(:)p Fz(\(\()p Fr(z)18 b(x)p Fz(\))1750
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5967
4634 y Fg(\001)1789 4625 y Fr(M)9 b Fz(\)\),)27 b(sa)n(y)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5968
b(.)27 b(A)n(t)h(this)f(p)r(oin)n(t,)h(the)g(simplicit)n(y)f(of)h(the)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5969
523 4725 y(pro)r(of)23 b(using)g(the)g(v)-5 b(ariable)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5970
b(con)n(v)n(en)n(tion)g(disapp)r(ears:)g(the)i(inductiv)n(e)f(h)n(yp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5971
(othesis)g(is)g(m)n(uc)n(h)523 4825 y(harder)36 b(to)i(sho)n(w)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5972
(applicable)g(b)r(ecause)g(it)h(men)n(tions)f Fr(M)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5973
b Fz(,)38 b(but)g(the)g(desired)f(goal)f(is)i(in)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5974
4924 y(terms)27 b(of)h(\()p Fr(z)17 b(x)p Fz(\))1016
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5975
4933 y Fg(\001)1055 4924 y Fr(M)9 b Fz(.)p Black Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5976
eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5977
%%Page: 13 13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5978
TeXDict begin 13 12 bop Black 1347 232 a Fw(Barendregt's)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5979
b(V)-6 b(ariable)26 b(Con)n(v)n(en)n(tion)f(in)h(Rule)f(Inductions)198
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5980
b(13)p Black Black Black Black 552 417 a Fv(lemma)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5981
b Fk(we)l(akening)7 b Fw(:)662 509 y Fv(assumes)26 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5982
Fk(a)1045 517 y Fx(1)1080 509 y Fw(:)i Fn(\000)38 b Fm(`)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5983
b Fk(M)12 b Fw(:)p Fk(T)37 b Fv(and)28 b Fk(a)1696 517
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5984
y Fx(2)1730 509 y Fw(:)g Fn(\000)38 b Fm(\022)27 b Fn(\000)2018
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5985
477 y Fl(0)2059 509 y Fv(and)h Fk(a)2273 517 y Fx(3)2307
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5986
509 y Fw(:)g Fk(valid)35 b Fn(\000)2614 477 y Fl(0)662
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5987
600 y Fv(sho)n(ws)27 b Fn(\000)980 568 y Fl(0)1021 600
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5988
y Fm(`)g Fk(M)12 b Fw(:)p Fk(T)552 691 y Fv(using)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5989
b Fk(a)826 699 y Fx(1)888 691 y Fk(a)933 699 y Fx(2)995
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5990
691 y Fk(a)1040 699 y Fx(3)552 782 y Fv(pro)r(of)37 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5991
Fw(\()p Fk(nominal-induct)e Fn(\000)j Fk(M)28 b(T)f(avoiding)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5992
b Fw(:)28 b Fn(\000)2025 751 y Fl(0)2066 782 y Fk(rule)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5993
b Fw(:)28 b Fk(str)l(ong-)r(typing-)r(induct)7 b Fw(\))662
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5994
874 y Fv(case)27 b Fw(\()p Fk(T)-6 b(yp)l(e)1039 882
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5995
y Fx(3)1101 874 y Fk(x)37 b Fn(\000)h Fk(T)1323 882 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5996
Fx(1)1385 874 y Fk(T)1450 882 y Fx(2)1512 874 y Fk(M)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5997
b Fw(\))662 965 y Fv(ha)n(v)n(e)26 b Fk(vc)t Fw(:)i Fk(x)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5998
b Fw(#)p Fn(\000)1161 933 y Fl(0)1203 965 y Fv(b)n(y)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5999
b Fk(fact)g Fw(|)f(v)l(ariable)g(con)n(v)n(en)n(tion)639
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6000
1056 y Fv(ha)n(v)n(e)20 b Fk(ih)6 b Fw(:)22 b(\()p Fk(x)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6001
b Fw(:)p Fk(T)1107 1064 y Fx(1)1142 1056 y Fw(\)::)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6002
Fn(\000)i Fm(\022)p Fw(\()p Fk(x)e Fw(:)p Fk(T)1492 1064
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6003
y Fx(1)1527 1056 y Fw(\)::)p Fn(\000)1665 1025 y Fl(0)1679
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6004
1056 y Fw(=)-13 b Fm(\))p Fk(valid)29 b Fw(\(\()p Fk(x)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6005
b Fw(:)p Fk(T)2179 1064 y Fx(1)2214 1056 y Fw(\)::)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6006
Fn(\000)2353 1025 y Fl(0)2366 1056 y Fw(\)=)-13 b Fm(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6007
Fw(\()p Fk(x)9 b Fw(:)p Fk(T)2680 1064 y Fx(1)2715 1056
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6008
y Fw(\)::)p Fn(\000)2854 1025 y Fl(0)2867 1056 y Fm(`)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6009
Fk(M)j Fw(:)p Fk(T)3081 1064 y Fx(2)3137 1056 y Fv(b)n(y)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6010
b Fk(fact)662 1148 y Fv(ha)n(v)n(e)k Fn(\000)38 b Fm(\022)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6011
b Fn(\000)1102 1116 y Fl(0)1143 1148 y Fv(b)n(y)g Fk(fact)662
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6012
1239 y Fv(then)g(ha)n(v)n(e)f Fw(\()p Fk(x)9 b Fw(:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6013
Fk(T)1224 1247 y Fx(1)1259 1239 y Fw(\)::)p Fn(\000)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6014
b Fm(\022)27 b Fw(\()p Fk(x)9 b Fw(:)p Fk(T)1664 1247
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6015
y Fx(1)1699 1239 y Fw(\)::)p Fn(\000)1837 1207 y Fl(0)1879
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6016
1239 y Fv(b)n(y)26 b Fk(simp)662 1330 y Fv(moreo)n(v)n(er)662
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6017
1422 y(ha)n(v)n(e)g Fk(valid)34 b Fn(\000)1122 1390 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6018
Fl(0)1163 1422 y Fv(b)n(y)27 b Fk(fact)662 1513 y Fv(then)g(ha)n(v)n(e)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6019
f Fk(valid)35 b Fw(\(\()p Fk(x)9 b Fw(:)p Fk(T)1446 1521
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6020
y Fx(1)1481 1513 y Fw(\)::)p Fn(\000)1619 1481 y Fl(0)1633
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6021
1513 y Fw(\))28 b Fv(using)g Fk(vc)k Fv(b)n(y)c Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6022
Fk(simp)f(add)8 b Fw(:)28 b Fk(valid-)q(c)l(ons)6 b Fw(\))662
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6023
1604 y Fv(ultimately)30 b(ha)n(v)n(e)c Fw(\()p Fk(x)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6024
b Fw(:)p Fk(T)1448 1612 y Fx(1)1483 1604 y Fw(\)::)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6025
Fn(\000)1621 1573 y Fl(0)1662 1604 y Fm(`)28 b Fk(M)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6026
b Fw(:)p Fk(T)1904 1612 y Fx(2)1966 1604 y Fv(using)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6027
b Fk(ih)33 b Fv(b)n(y)27 b Fk(simp)662 1696 y Fv(with)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6028
Fk(vc)k Fv(sho)n(w)c Fn(\000)1248 1664 y Fl(0)1289 1696
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6029
y Fm(`)f Fk(lam)6 b Fw(\()p Fk(x)j Fn(:)p Fk(M)j Fw(\))27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6030
b(:)h Fk(T)1838 1704 y Fx(1)1900 1696 y Fm(!)f Fk(T)2069
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6031
1704 y Fx(2)2131 1696 y Fv(b)n(y)g Fk(auto)552 1787 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6032
Fv(qed)g Fw(\()p Fk(auto)5 b Fw(\))28 b(|)d(cases)i(T)n(yp)r(e)1421
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6033
1795 y Fx(1)1481 1787 y Fw(and)e(T)n(yp)r(e)1803 1795
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6034
y Fx(2)523 1927 y Fv(Fig.)15 b(1.)32 b Fw(A)f(readable)i(Isab)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6035
(elle-Isar)h(pro)r(of)f(for)g(the)f(w)n(eak)n(ening)g(lemma)f(using)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6036
(the)f(strong)g(in-)523 2018 y(duction)j(principle)h(of)h(the)e(t)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6037
(yping)g(relation.)i(The)f(stronger)h(induction)e(principle)h(allo)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6038
(ws)i(us)523 2109 y(to)31 b(assume)g(a)h(v)l(ariable)f(con)n(v)n(en)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6039
(tion,)g(in)g(this)g(pro)r(of)h Fn(x)e Fw(#)g Fn(\000)2349
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6040
2077 y Fl(0)2371 2109 y Fw(,)i(whic)n(h)f(mak)n(es)f(the)h(pro)r(of)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6041
(to)f(go)523 2200 y(through)25 b(without)h(di\016culties.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6042
Black 523 2508 a Ft(5.2)95 b(P)m(arallel)31 b(Reduction)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6043
2728 y Fz(In)h([2],)f(the)h(cen)n(tral)f(lemma)h(of)f(the)h(pro)r(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6044
(for)f(the)h(Ch)n(urc)n(h-Rosser)d(prop)r(ert)n(y)h(of)i(b)r(eta-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6045
2827 y(reduction)27 b(is)h(the)g(substitutivit)n(y)h(prop)r(ert)n(y)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6046
(of)i(the)g Fp(\000)-14 b(!)2286 2845 y Fo(1)2241 2827
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6047
y Fp(\000)f(!)p Fz(-reduction.)28 b(T)-7 b(o)27 b(formalise)g(this)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6048
2927 y(pro)r(of)g(while)h(preserving)e(the)i(informal)f(v)n(ersion's)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6049
(simplicit)n(y)-7 b(,)27 b(w)n(e)h(will)g(need)f(the)h(strong)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6050
3027 y(induction)g(principle)g(for)f Fp(\000)-15 b(!)1434
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6051
3045 y Fo(1)1389 3027 y Fp(\000)g(!)q Fz(.)648 3129 y(Before)18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6052
b(pro)r(ceeding,)h(w)n(e)g(need)h(t)n(w)n(o)e(imp)r(ortan)n(t)i(prop)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6053
(erties)e(of)i(the)g(substitution)g(func-)523 3220 y(tion,)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6054
b(whic)n(h)f(o)r(ccurs)g(in)h(the)g(redex)f(rule)g(One)2003
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6055
3232 y Fy(4)2040 3220 y Fz(.)h(W)-7 b(e)30 b(c)n(haracterise)d(the)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6056
(action)g(of)f(a)g(p)r(er-)523 3311 y(m)n(utation)41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6057
b(o)n(v)n(er)e(a)i(substitution)g(\(sho)n(wing)f(that)i(substitution)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6058
(is)g(equiv)-5 b(arian)n(t\),)40 b(and)523 3403 y(the)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6059
b(supp)r(ort)e(of)i(a)e(substitution.)i(Both)f(pro)r(ofs)f(are)g(b)n(y)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6060
h(straigh)n(tforw)n(ard)d(v)n(c-compatible)523 3494 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6061
Fs(structur)l(al)35 b Fz(induction)28 b(o)n(v)n(er)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6062
Fr(M)9 b Fz(:)1184 3688 y Fn(\031)1231 3697 y Fg(\001)1269
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6063
3688 y Fw(\()p Fn(M)f Fw([)p Fn(x)21 b Fw(:=)g Fn(N)8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6064
b Fw(]\))22 b(=)g(\()p Fn(\031)1870 3697 y Fg(\001)1907
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6065
3688 y Fn(M)8 b Fw(\)[\()p Fn(\031)2117 3697 y Fg(\001)2155
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6066
3688 y Fn(x)p Fw(\))21 b(:=)g(\()p Fn(\031)2429 3697
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6067
y Fg(\001)2467 3688 y Fn(N)8 b Fw(\)])p Black 681 w(\(23\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6068
Black 1128 3804 a Fc(supp)q Fw(\()p Fn(M)g Fw([)p Fn(x)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6069
b Fw(:=)f Fn(N)8 b Fw(]\))22 b Fm(\022)f Fw(\()p Fc(supp)q
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6070
Fw(\()p Fn(M)8 b Fw(\))17 b Fm(\000)g(f)p Fn(x)p Fm(g)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6071
Fw(\))g Fm([)g Fc(supp)q Fw(\()p Fn(N)8 b Fw(\))p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6072
515 w(\(24\))p Black 648 4017 a Fz(With)21 b(this)g(w)n(e)g(can)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6073
(start)h(to)g(c)n(hec)n(k)f(the)h(v)n(c-compatibilit)n(y)f(conditions:)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6074
g(the)h(condition)523 4117 y(ab)r(out)d(equiv)-5 b(ariance)18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6075
b(of)g(functions)h(and)f(side-conditions)g(is)g(again)f(easily)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6076
(con\014rmed.)g(The)523 4216 y(second)28 b(condition)g(is)g(that)g(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6077
(ound)h(v)-5 b(ariables)27 b(are)g(free)h(in)g(the)h(relation's)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6078
(rules')h(conclu-)523 4316 y(sions.)33 b(In)h(rule)f(One)1186
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6079
4328 y Fy(2)1223 4316 y Fz(,)h(this)g(is)g(trivial)f(b)r(ecause)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6080
Fr(y)j Fz(#)d Fs(lam)7 b Fz(\()p Fr(y)s(:M)i Fz(\))34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6081
b(and)f Fr(y)j Fz(#)e Fs(lam)7 b Fz(\()p Fr(y)s(:M)3350
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6082
4286 y Fj(0)3373 4316 y Fz(\))523 4416 y(hold.)36 b(A)g(problem)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6083
(arises,)e(ho)n(w)n(ev)n(er,)g(with)j(rule)f(One)2298
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6084
4428 y Fy(4)2334 4416 y Fz(.)h(Here)e(w)n(e)h(ha)n(v)n(e)f(to)h(sho)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6085
(w)f(that)523 4515 y Fr(y)f Fz(#)d Fs(app)6 b Fz(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6086
Fs(lam)h Fz(\()p Fr(y)s(:M)i Fz(\))p Fr(;)14 b(N)9 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6087
Fz(\))33 b(and)f Fr(y)h Fz(#)e Fr(M)1829 4485 y Fj(0)1852
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6088
4515 y Fz([)p Fr(y)j Fz(:=)c Fr(N)2144 4485 y Fj(0)2167
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6089
4515 y Fz(],)j(and)f(w)n(e)g(ha)n(v)n(e)f(no)h(assumptions)f(to)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6090
4615 y(hand)d(ab)r(out)f Fr(y)s Fz(.)648 4725 y(It)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6091
b(is)g(certainly)g(true)g(that)g Fr(y)j Fz(is)d(fresh)g(for)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6092
Fs(lam)7 b Fz(\()p Fr(y)s(:M)i Fz(\),)23 b(but)f(it)h(ma)n(y)e(o)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6093
(ccur)h(in)g Fr(N)9 b Fz(.)22 b(As)h(for)523 4825 y(the)k(term)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6094
Fr(M)953 4795 y Fj(0)976 4825 y Fz([)p Fr(y)f Fz(:=)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6095
Fr(N)1253 4795 y Fj(0)1276 4825 y Fz(],)k(w)n(e)g(kno)n(w)f(that)h(an)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6096
(y)f(o)r(ccurrences)g(of)g Fr(y)k Fz(in)d Fr(M)2818 4795
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6097
y Fj(0)2868 4825 y Fz(will)h(b)r(e)f(mask)n(ed)523 4924
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6098
y(b)n(y)g(the)h(substitution)g(\(see)g(\(24\)\),)g(but)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6099
Fr(y)i Fz(ma)n(y)d(still)h(b)r(e)g(free)f(in)h Fr(N)2651
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6100
4894 y Fj(0)2674 4924 y Fz(.)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6101
%%Page: 14 14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6102
TeXDict begin 14 13 bop Black 523 232 a Fw(14)199 b(Christian)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6103
b(Urban,)e(Stefan)h(Berghofer,)i(and)d(Mic)n(hael)i(Norrish)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6104
Black 648 448 a Fz(W)-7 b(e)28 b(need)f(to)h(reform)n(ulate)e(One)1677
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6105
460 y Fy(4)1742 448 y Fz(to)h(read)1143 584 y Fn(y)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6106
Fw(#)d Fn(N)85 b(y)24 b Fw(#)e Fn(N)1653 552 y Fl(0)1752
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6107
584 y Fn(M)30 b Fm(\000)-13 b(!)1925 600 y Fo(1)1884
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6108
584 y Fm(\000)g(!)21 b Fn(M)2111 552 y Fl(0)2210 584
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6109
y Fn(N)30 b Fm(\000)-13 b(!)2370 600 y Fo(1)2329 584
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6110
y Fm(\000)g(!)22 b Fn(N)2544 552 y Fl(0)p 1143 618 1424
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6111
4 v 1247 694 a Fk(app)6 b Fw(\()p Fk(lam)f Fw(\()p Fn(y)s(:M)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6112
Fw(\))p Fn(;)13 b(N)8 b Fw(\))21 b Fm(\000)-13 b(!)1954
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6113
710 y Fo(1)1914 694 y Fm(\000)f(!)22 b Fn(M)2141 663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6114
y Fl(0)2163 694 y Fw([)p Fn(y)j Fw(:=)c Fn(N)2418 663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6115
y Fl(0)2441 694 y Fw(])2608 642 y(One)2744 610 y Fl(00)2744
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6116
655 y Fx(4)523 849 y Fz(so)27 b(that)g(the)h(v)n(c-compatibilit)n(y)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6117
(conditions)h(can)g(b)r(e)h(disc)n(harged.)d(In)j(other)f(w)n(ords,)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6118
(if)h(w)n(e)523 949 y(ha)n(v)n(e)19 b(rule)h(One)1014
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6119
919 y Fj(00)1014 970 y Fy(4)1077 949 y Fz(w)n(e)f(can)h(apply)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6120
(Theorem)g(1,)g(but)h(not)f(if)h(w)n(e)f(use)g(One)2739
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6121
961 y Fy(4)2776 949 y Fz(.)g(This)g(is)g(anno)n(ying)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6122
1049 y(b)r(ecause)34 b(b)r(oth)h(v)n(ersions)d(can)j(b)r(e)f(sho)n(wn)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6123
(to)g(de\014ne)h(the)g(same)f(relation,)f(but)i(w)n(e)f(ha)n(v)n(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6124
1148 y(no)26 b(general,)f(and)i(automatable,)e(metho)r(d)i(for)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6125
(determining)g(this.)h(F)-7 b(or)26 b(the)h(momen)n(t,)f(w)n(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6126
1248 y(reject)34 b(rule)g(One)1079 1260 y Fy(4)1150 1248
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6127
y Fz(and)g(require)f(the)h(user)g(of)g(the)g(nominal)g(datat)n(yp)r(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6128
(pac)n(k)-5 b(age)32 b(to)i(use)523 1348 y(One)671 1317
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6129
y Fj(00)671 1368 y Fy(4)713 1348 y Fz(.)28 b(If)g(this)g(is)f(done,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6130
(the)g(substitutivit)n(y)g(lemma)f(is)h(almost)f(automatic:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6131
Black Black 566 1480 a Fv(lemma)g Fk(substitutivity-)s(aux)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6132
b Fw(:)621 1571 y Fv(assumes)27 b Fk(a)6 b Fw(:)27 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6133
Fk(N)12 b Fm(\000)-13 b(!)1246 1579 y Fx(1)1281 1571
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6134
y Fk(N)1358 1539 y Fl(0)621 1662 y Fv(sho)n(ws)27 b Fk(M)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6135
b Fw([)p Fk(x)d Fw(:=)p Fk(N)j Fw(])28 b Fm(\000)-13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6136
b(!)1342 1670 y Fx(1)1404 1662 y Fk(M)12 b Fw([)p Fk(x)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6137
Fw(:=)p Fk(N)1709 1631 y Fl(0)1723 1662 y Fw(])566 1754
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6138
y Fv(using)29 b Fk(a)k Fv(b)n(y)28 b Fw(\()p Fk(nominal-induct)g(M)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6139
(avoiding)7 b Fw(:)28 b Fk(x)g(N)g(N)2208 1722 y Fl(0)2249
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6140
1754 y Fk(rule)6 b Fw(:)28 b Fk(str)l(ong-)r(lam-induct)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6141
b Fw(\))29 b(\()p Fk(auto)5 b Fw(\))566 1886 y Fv(lemma)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6142
b Fk(subtitutivity)7 b Fw(:)621 1977 y Fv(assumes)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6143
b Fk(a)1005 1985 y Fx(1)1039 1977 y Fw(:)h Fk(M)12 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6144
Fm(\000)-13 b(!)1293 1985 y Fx(1)1327 1977 y Fk(M)1416
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6145
1945 y Fl(0)1458 1977 y Fv(and)27 b Fk(a)1671 1985 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6146
Fx(2)1706 1977 y Fw(:)h Fk(N)12 b Fm(\000)-13 b(!)1948
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6147
1985 y Fx(1)1982 1977 y Fk(N)2059 1945 y Fl(0)621 2068
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6148
y Fv(sho)n(ws)27 b Fk(M)12 b Fw([)p Fk(x)d Fw(:=)p Fk(N)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6149
Fw(])p Fm(\000)-12 b(!)1315 2076 y Fx(1)1349 2068 y Fk(M)1438
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6150
2037 y Fl(0)1452 2068 y Fw([)p Fk(x)9 b Fw(:=)p Fk(N)1677
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6151
2037 y Fl(0)1690 2068 y Fw(])566 2160 y Fv(using)21 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6152
Fk(a)833 2168 y Fx(1)889 2160 y Fk(a)934 2168 y Fx(2)989
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6153
2160 y Fv(b)n(y)f Fw(\()p Fk(nominal-induct)h(M)g(M)1838
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6154
2128 y Fl(0)1872 2160 y Fk(avoiding)7 b Fw(:)21 b Fk(N)f(N)2353
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6155
2128 y Fl(0)2388 2160 y Fk(x)g(rule)6 b Fw(:)21 b Fk(str)l(ong-)r(p)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6156
(ar)l(al)t(lel-)q(induct)7 b Fw(\))1205 2251 y(\()p Fk(auto)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6157
b(simp)e(add)8 b Fw(:)26 b Fk(substitutivity-)s(aux)h(substitution-)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6158
(lemma)e(fr)l(esh-)r(atm)6 b Fw(\))523 2387 y Fz(The)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6159
b(\014rst)g(lemma)g(is)h(pro)n(v)n(ed)d(b)n(y)i(a)g(v)n(c-compatible)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6160
Fs(structur)l(al)37 b Fz(induction)29 b(o)n(v)n(er)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6161
Fr(M)9 b Fz(;)29 b(the)523 2487 y(second,)39 b(the)h(actual)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6162
(substitutivit)n(y)i(prop)r(ert)n(y)-7 b(,)38 b(is)i(pro)n(v)n(ed)e(b)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6163
(y)h(a)g(v)n(c-compatible)g Fs(rule)523 2586 y Fz(induction)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6164
b(relying)e(on)h(the)g(substitution)h(lemma,)f(and)h(the)f(lemma)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6165
Fs(fr)l(esh-atm)p Fz(,)h(whic)n(h)523 2686 y(states)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6166
b(that)h Fr(x)c Fz(#)f Fr(y)30 b Fz(is)e(the)g(same)f(as)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6167
Fr(x)c Fp(6)p Fz(=)g Fr(y)30 b Fz(when)e Fr(y)i Fz(is)e(an)f(atom.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6168
2936 y Fu(6)112 b(Related)37 b(W)-9 b(ork)523 3121 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6169
Fz(Apart)28 b(from)g(our)g(o)n(wn)g(preliminary)f(w)n(ork)g(in)i(this)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6170
(area)f([10],)h(w)n(e)g(b)r(eliev)n(e)g(the)h(prettiest)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6171
3220 y(formal)35 b(pro)r(of)g(of)g(the)h(w)n(eak)n(ening)e(lemma)h(to)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6172
(b)r(e)g(that)f(in)h(Pitts)g([8].)f(This)g(pro)r(of)g(uses)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6173
3320 y(the)d(equiv)-5 b(ariance)29 b(prop)r(ert)n(y)h(of)h(the)h(t)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6174
(yping)f(relation,)f(and)h(includes)g(a)g(renaming)f(step)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6175
3419 y(using)25 b(p)r(erm)n(utations.)h(Because)e(of)i(the)g(pleasan)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6176
(t)f(prop)r(erties)f(that)i(p)r(erm)n(utations)g(enjo)n(y)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6177
3519 y(\(they)j(are)f(bijectiv)n(e)h(renamings,)e(in)i(con)n(trast)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6178
(to)i(substitutions)f(whic)n(h)h(migh)n(t)f(iden)n(tify)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6179
3619 y(t)n(w)n(o)k(names\),)g(the)h(renaming)f(can)g(b)r(e)h(done)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6180
(with)g(relativ)n(ely)e(minimal)i(o)n(v)n(erhead.)e(Our)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6181
3718 y(con)n(tribution)20 b(is)g(that)g(w)n(e)g(ha)n(v)n(e)f(built)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6182
(this)g(renaming)e(in)n(to)h(our)g(v)n(c-compatible)f(induction)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6183
3818 y(principles)k(once)f(and)g(for)h(all.)f(Pro)r(ofs)g(using)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6184
(v)n(c-compatible)f(principles)g(then)i(do)e(not)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6185
3918 y(need)28 b(to)f(p)r(erform)g(an)n(y)g(explicit)h(renaming)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6186
(steps.)648 4009 y(Somewhat)i(similar)g(to)h(our)f(approac)n(h)g(is)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6187
(the)i(w)n(ork)d(of)i(P)n(ollac)n(k)e(and)i(McKinna)f([6].)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6188
4100 y(Starting)c(from)g(the)g(standard)f(induction)i(principle)f(that)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6189
g(is)h(asso)r(ciated)d(with)j(an)f(induc-)523 4192 y(tiv)n(e)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6190
(de\014nition,)g(w)n(e)g(deriv)n(ed)f(an)h(induction)h(principle)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6191
(that)g(allo)n(ws)f(em)n(ulation)g(of)h(Baren-)523 4283
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6192
y(dregt's)33 b(v)-5 b(ariable)33 b(con)n(v)n(en)n(tion.)g(P)n(ollac)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6193
(k)e(and)j(McKinna,)g(in)g(con)n(trast,)e(ga)n(v)n(e)h(a)g(\\w)n(eak")
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6194
523 4374 y(and)26 b(\\strong")e(v)n(ersion)h(of)i(the)f(t)n(yping)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6195
(relation.)g(These)g(v)n(ersions)f(di\013er)h(in)h(the)f(w)n(a)n(y)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6196
(the)523 4466 y(rule)h(for)g(abstractions)f(is)i(stated:)1228
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6197
4585 y Fn(x)21 b Fw(#)g Fn(M)85 b Fw(\()p Fn(x)21 b Fw(:)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6198
Fn(T)1719 4593 y Fx(1)1754 4585 y Fw(\))g(::)h Fn(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6199
b Fm(`)21 b Fn(M)8 b Fw([)p Fn(y)25 b Fw(:=)c Fn(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6200
Fw(])g(:)h Fn(T)2458 4593 y Fx(2)p 1228 4624 1265 4 v
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6201
1450 4697 a Fn(\000)32 b Fm(`)21 b Fk(lam)5 b Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6202
Fn(y)s(:M)j Fw(\))21 b(:)h Fn(T)2037 4705 y Fx(1)2093
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6203
4697 y Fm(!)f Fn(T)2236 4705 y Fx(2)2534 4650 y Fw(w)n(eak)1133
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6204
4827 y Fm(8)p Fn(x:)g(x)f Fw(#)i Fn(\000)32 b Fm(\))21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6205
b Fw(\()p Fn(x)g Fw(:)g Fn(T)1771 4835 y Fx(1)1806 4827
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6206
y Fw(\))g(::)h Fn(\000)32 b Fm(`)21 b Fn(M)8 b Fw([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6207
Fn(y)24 b Fw(:=)e Fn(x)p Fw(])f(:)h Fn(T)2510 4835 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6208
Fx(2)p 1133 4866 1412 4 v 1428 4938 a Fn(\000)32 b Fm(`)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6209
b Fk(lam)6 b Fw(\()p Fn(y)s(:M)i Fw(\))21 b(:)g Fn(T)2015
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6210
4946 y Fx(1)2071 4938 y Fm(!)g Fn(T)2214 4946 y Fx(2)2586
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6211
4882 y Fw(strong)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6212
%%Page: 15 15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6213
TeXDict begin 15 14 bop Black 1347 232 a Fw(Barendregt's)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6214
b(V)-6 b(ariable)26 b(Con)n(v)n(en)n(tion)f(in)h(Rule)f(Inductions)198
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6215
b(15)p Black 523 448 a Fz(They)27 b(then)h(sho)n(w)n(ed)f(that)g(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6216
(oth)h(v)n(ersions)e(deriv)n(e)h(the)g(same)g(t)n(yping)h(judgemen)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6217
(ts.)f(With)523 548 y(this)h(they)g(pro)n(v)n(ed)e(the)i(w)n(eak)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6218
(ening)e(lemma)i(using)f(the)h(\\strong")e(v)n(ersion)g(of)h(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6219
(princi-)523 648 y(ple,)23 b(while)h(kno)n(wing)e(that)h(the)h(result)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6220
(held)g(for)g(the)g(\\w)n(eak")e(relation)h(as)h(w)n(ell.)g(The)g(main)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6221
523 747 y(di\013erence)32 b(b)r(et)n(w)n(een)g(this)g(and)g(our)f(w)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6222
(ork)g(seems)g(to)h(b)r(e)g(of)g(con)n(v)n(enience:)f(w)n(e)h(can)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6223
(rela-)523 847 y(tiv)n(ely)g(easily)f(deriv)n(e,)h(in)g(a)g(uniform)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6224
(w)n(a)n(y)-7 b(,)30 b(an)h(induction)g(principle)h(for)e(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6225
(c-compatible)523 946 y(relations)22 b(\(w)n(e)i(ha)n(v)n(e)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6226
(illustrated)h(this)h(p)r(oin)n(t)g(with)g(t)n(w)n(o)f(examples\).)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6227
(Ac)n(hieving)g(the)h(same)523 1046 y(uniformit)n(y)c(in)h(the)f(st)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6228
(yle)g(of)g(McKinna)g(and)g(P)n(ollac)n(k)e(do)r(es)i(not)g(seem)g(as)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6229
(straigh)n(tforw)n(ard.)523 1306 y Fu(7)112 b(F)-9 b(uture)38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6230
b(W)-9 b(ork)523 1492 y Fz(Our)24 b(future)g(w)n(ork)f(will)i(concen)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6231
(trate)e(on)h(t)n(w)n(o)g(asp)r(ects:)g(\014rst)g(on)g(generalising)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6232
(our)i(de\014ni-)523 1583 y(tion)e(of)f(sc)n(hematic)g(rules)g(so)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6233
(that)h(they)g(ma)n(y)-7 b(,)21 b(for)g(example,)g(include)h(quan)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6234
(ti\014ers.)e(Second)523 1675 y(on)34 b(b)r(eing)h(more)e(lib)r(eral)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6235
(ab)r(out)g(whic)n(h)h(v)-5 b(ariables)33 b(can)h(b)r(e)g(included)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6236
(in)g(the)g(induction)523 1766 y(con)n(text.)d(T)-7 b(o)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6237
b(see)g(what)g(w)n(e)g(ha)n(v)n(e)g(in)g(mind)h(with)g(this,)g(recall)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6238
(that)i(w)n(e)f(allo)n(w)n(ed)f(in)i(the)523 1857 y(induction)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6239
b(con)n(text)f(only)h(v)-5 b(ariables)24 b(that)i(are)f(in)g(binding)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6240
(p)r(osition.)g(Ho)n(w)n(ev)n(er)e(there)h(are)523 1949
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6241
y(examples)k(where)g(this)h(is)g(to)r(o)f(restrictiv)n(e:)f(for)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6242
(example)f(Crary)f(giv)n(es)g(in)i([4,)f(P)n(age)f(231])523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6243
2040 y(the)38 b(follo)n(wing)f(m)n(utual)g(inductiv)n(e)h(de\014nition)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6244
g(for)f(the)h(judgemen)n(ts)g Fr(\000)51 b Fp(`)40 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6245
Fr(s)f Fp(,)h Fr(t)g Fz(:)g Fr(T)523 2131 y Fz(and)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6246
Fr(\000)52 b Fp(`)41 b Fr(p)f Fp($)h Fr(q)i Fz(:)e Fr(T)49
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6247
b Fz(\(they)39 b(represen)n(t)e(a)h(t)n(yp)r(e-driv)n(en)f(equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6248
b(alence)38 b(algorithm)f(for)523 2223 y(lam)n(b)r(da-terms)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6249
b(with)h(constan)n(ts\):)523 2377 y Fn(s)21 b Fm(+)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6250
Fn(p)77 b(t)21 b Fm(+)g Fn(q)80 b(\000)32 b Fm(`)21 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6251
Fn(p)g Fm($)g Fn(q)j Fw(:)e Fn(T)p 523 2411 934 4 v 776
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6252
2480 a(\000)32 b Fm(`)21 b Fn(s)h Fm(,)f Fn(t)g Fw(:)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6253
Fn(b)1472 2433 y Fw(Ae)1564 2441 y Fx(1)1641 2373 y Fw(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6254
Fn(x)g Fw(:)h Fn(T)1824 2381 y Fx(1)1858 2373 y Fw(\))9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6255
b(::)g Fn(\000)32 b Fm(`)21 b Fn(s)g(x)g Fm(,)g Fn(t)g(x)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6256
Fw(:)h Fn(T)2517 2381 y Fx(2)p 1641 2411 910 4 v 1760
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6257
2480 a Fn(\000)32 b Fm(`)21 b Fn(s)g Fm(,)g Fn(t)g Fw(:)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6258
Fn(T)2199 2488 y Fx(1)2255 2480 y Fm(!)f Fn(T)2398 2488
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6259
y Fx(2)2567 2433 y Fw(Ae)2659 2441 y Fx(2)p 2736 2411
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6260
539 4 v 2736 2480 a Fn(\000)32 b Fm(`)21 b Fn(s)g Fm(,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6261
Fn(t)g Fw(:)h Fn(unit)3290 2433 y Fw(Ae)3382 2441 y Fx(3)675
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6262
2611 y Fw(\()p Fn(x)f Fw(:)h Fn(T)11 b Fw(\))20 b Fm(2)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6263
Fn(\000)p 626 2649 474 4 v 626 2718 a(\000)32 b Fm(`)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6264
b Fn(x)g Fm($)g Fn(x)g Fw(:)h Fn(T)1115 2671 y Fw(P)n(e)1199
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6265
2679 y Fx(1)1298 2615 y Fn(\000)32 b Fm(`)21 b Fn(p)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6266
Fm($)g Fn(q)j Fw(:)e Fn(T)1749 2623 y Fx(1)1805 2615
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6267
y Fm(!)f Fn(T)1948 2623 y Fx(2)2059 2615 y Fn(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6268
b Fm(`)21 b Fn(s)g Fm($)g Fn(t)g Fw(:)h Fn(T)2498 2623
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6269
y Fx(1)p 1298 2649 1235 4 v 1619 2718 a Fn(\000)32 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6270
Fm(`)21 b Fn(p)g(s)g Fm($)h Fn(q)i(t)d Fw(:)h Fn(T)2177
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6271
2726 y Fx(2)2548 2671 y Fw(P)n(e)2633 2679 y Fx(2)p 2731
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6272
2649 448 4 v 2731 2718 a Fn(\000)32 b Fm(`)21 b Fn(k)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6273
Fm($)d Fn(k)j Fw(:)d Fn(b)3195 2671 y Fw(P)n(e)3279 2679
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6274
y Fx(3)523 2876 y Fz(What)35 b(is)f(in)n(teresting)g(is)g(that)h(these)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6275
f(rules)g(do)g(not)g(con)n(tain)g(an)n(y)g(v)-5 b(ariable)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6276
b(in)i(binding)523 2976 y(p)r(osition.)j(Still,)h(in)f(some)g(pro)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6277
(ofs)f(b)n(y)h(induction)g(o)n(v)n(er)f(those)g(rules)h(one)f(w)n(an)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6278
(ts)h(to)g(b)r(e)523 3075 y(able)g(to)f(assume)g(that)i(the)f(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6279
b(ariable)37 b Fr(x)h Fz(in)g(the)h(rule)e(Ae)2404 3087
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6280
y Fy(2)2479 3075 y Fz(satis\014es)h(certain)f(freshness)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6281
3175 y(conditions.)c(Our)g(implemen)n(tation)g(already)f(deals)h(with)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6282
(this)g(situation)f(b)n(y)g(explicitly)523 3275 y(giving)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6283
b(the)h(information)g(that)g Fr(x)g Fz(should)g(app)r(ear)f(in)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6284
(induction)g(con)n(text.)g(Ho)n(w)n(ev)n(er,)523 3374
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6285
y(w)n(e)g(ha)n(v)n(e)g(not)g(y)n(et)h(w)n(ork)n(ed)e(out)h(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6286
(theory)-7 b(.)523 3635 y Fu(8)112 b(Conclusion)523 3828
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6287
y Fz(In)22 b(the)h Fa(POPLmark)d Fz(Challenge)i([1],)g(the)g(pro)r(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6288
(of)h(the)h(w)n(eak)n(ening)d(lemma)i(is)g(describ)r(ed)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6289
3928 y(as)j(a)h(\\straigh)n(tforw)n(ard)d(induction".)j(In)g(fact,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6290
(mec)n(hanising)f(this)h(informal)g(pro)r(of)f(is)h Fs(not)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6291
4028 y Fz(straigh)n(tforw)n(ard)38 b(at)j(all)g(\(see)g(for)f(example)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6292
([6,)13 b(5,)g(8]\).)41 b(W)-7 b(e)42 b(ha)n(v)n(e)e(giv)n(en)g(a)g(no)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6293
n(v)n(el)g(rule)523 4127 y(induction)d(principle)h(for)e(the)h(t)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6294
(yping)g(relation)f(that)i(mak)n(es)e(pro)n(ving)f(the)j(w)n(eak)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6295
(ening)523 4227 y(lemma)28 b(mec)n(hanically)e(as)h(simple)h(as)f(p)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6296
(erforming)f(the)i(informal)f(pro)r(of.)648 4327 y(Imp)r(ortan)n(tly)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6297
b(,)34 b(this)h(new)g(principle)g(can)g(b)r(e)g(deriv)n(ed)f(from)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6298
(the)g(original)f(inductiv)n(e)523 4426 y(de\014nition)c(of)f(the)h(t)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6299
(yping)f(relation)f(in)i(a)f(mec)n(hanical)f(w)n(a)n(y)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6300
b(.)28 b(This)i(metho)r(d)f(extends)h(our)523 4526 y(earlier)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6301
b(w)n(ork)g([10,)13 b(7],)25 b(where)g(w)n(e)g(constructed)g(our)g(new)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6302
g(induction)h(principles)f(b)n(y)g(hand.)523 4625 y(By)j(formally)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6303
(deriving)g(principles)h(that)g(a)n(v)n(oid)f(the)h(need)h(to)e(rename)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6304
h(b)r(ound)g(v)-5 b(ariables,)523 4725 y(w)n(e)24 b(adv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6305
b(ance)24 b(the)i(state-of-the-art)d(in)i(mec)n(hanical)e(theorem-pro)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6306
(ving)g(o)n(v)n(er)g(syn)n(tax)g(with)523 4825 y(binders.)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6307
b(The)g(results)g(of)g(this)h(pap)r(er)f(ha)n(v)n(e)f(already)g(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6308
(een)i(used)f(man)n(y)g(times)g(in)h(the)523 4924 y(nominal)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6309
b(datat)n(yp)r(e)g(pac)n(k)-5 b(age:)18 b(for)h(example)g(in)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6310
(pro)r(ofs)f(of)g(the)h(CR)g(and)f(SN)h(prop)r(erties)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6311
Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6312
%%Page: 16 16
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6313
TeXDict begin 16 15 bop Black 523 232 a Fw(16)199 b(Christian)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6314
b(Urban,)e(Stefan)h(Berghofer,)i(and)d(Mic)n(hael)i(Norrish)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6315
Black 523 448 a Fz(in)21 b(the)g Fr(\025)p Fz(-calculus,)f(in)h(pro)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6316
(ofs)f(ab)r(out)g(the)h(pi-calculus,)f(in)h(pro)r(ofs)e(ab)r(out)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6317
(logical)e(relations)523 548 y(and)27 b(in)h(sev)n(eral)e(pro)r(ofs)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6318
(from)g(structural)g(op)r(erational)f(seman)n(tics.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6319
648 y(The)32 b(fact)g(that)h(our)e(tec)n(hnique)i(ma)n(y)e(require)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6320
(users)f(to)h(cast)g(some)g(inductiv)n(e)g(de\014-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6321
747 y(nitions)g(in)g(alternativ)n(e)f(forms)h(is)f(unfortunate.)i(In)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6322
(the)g(earlier)f([10],)g(our)g(hand-pro)r(ofs)523 847
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6323
y(correctly)d(deriv)n(ed)h(a)g(v)n(c-compatible)f(principle)h(from)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6324
(the)h(original)e(de\014nition)i(of)f Fp(\000)-14 b(!)3294
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6325
865 y Fo(1)3248 847 y Fp(\000)g(!)p Fz(;)523 946 y(w)n(e)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6326
b(hop)r(e)h(that)g(future)g(w)n(ork)e(will)i(automatically)e(justify)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6327
(comparable)d(deriv)-5 b(ations.)523 1071 y Ft(Ac)m(kno)m(wledgemen)m
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6328
(ts)31 b Fz(W)-7 b(e)32 b(are)f(v)n(ery)g(grateful)g(to)h(Andrew)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6329
(Pitts)f(for)h(the)g(man)n(y)f(dis-)523 1171 y(cussions)c(with)h(him)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6330
(on)f(the)h(sub)5 b(ject)28 b(of)f(this)h(pap)r(er.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6331
1436 y Fu(References)p Black 561 1627 a Fw(1.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6332
43 w(B.)f(E.)h(Aydemir,)d(A.)i(Bohannon,)g(M.)h(F)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6333
b(airbairn,)28 b(J.)g(N.)e(F)-6 b(oster,)28 b(B.)g(C.)f(Pierce,)i(P)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6334
b(.)27 b(Sew)n(ell,)663 1719 y(D.)f(Vytiniotis,)g(G.)h(W)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6335
b(ash)n(burn,)25 b(S.)h(W)-6 b(eiric)n(h,)26 b(and)g(S.)g(Zdancewic.)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6336
b(Mec)n(hanized)27 b(Metathe-)663 1810 y(ory)i(for)i(the)e(Masses:)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6337
(The)f(P)n(opl)q(Mark)g(Challenge.)47 b(In)29 b Fk(Pr)l(o)l(c.)j(of)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6338
(the)j(18th)f(International)663 1901 y(Confer)l(enc)l(e)d(on)f(The)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6339
(or)l(em)h(Pr)l(oving)g(in)f(Higher-Or)l(der)i(L)l(o)l(gics)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6340
(\(TPHOLs\))p Fw(,)e(v)n(olume)e(3603)663 1993 y(of)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6341
Fk(LNCS)p Fw(,)g(pages)h(50{65,)h(2005.)p Black 561 2084
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6342
a(2.)p Black 43 w(H.)j(Barendregt.)53 b Fk(The)33 b(L)l(amb)l(da)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6343
(Calculus:)e(its)h(Syntax)i(and)e(Semantics)p Fw(,)g(v)n(olume)d(103)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6344
(of)663 2175 y Fk(Studies)28 b(in)f(L)l(o)l(gic)h(and)g(the)h(F)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6345
b(oundations)29 b(of)e(Mathematics)p Fw(.)36 b(North-Holland,)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6346
b(1981.)p Black 561 2267 a(3.)p Black 43 w(J.)i(Bengtson)g(and)e(J.)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6347
(P)n(arro)n(w.)40 b(F)-6 b(ormalising)28 b(the)f(pi-Calculus)h(using)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6348
(Nominal)e(Logic.)41 b(In)663 2358 y Fk(Pr)l(o)l(c.)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6349
b(of)f(the)h(10th)h(International)f(Confer)l(enc)l(e)h(on)f(F)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6350
b(oundations)24 b(of)e(Softwar)l(e)i(Scienc)l(e)f(and)663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6351
2449 y(Computation)28 b(Structur)l(es)j(\(F)n(OSSA)n(CS\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6352
Fw(,)c(v)n(olume)d(4423)k(of)e Fk(LNCS)p Fw(,)g(pages)h(63{77,)g(2007.)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6353
p Black 561 2540 a(4.)p Black 43 w(K.)22 b(Crary)-6 b(.)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6354
b Fk(A)l(dvanc)l(e)l(d)c(T)-6 b(opics)26 b(in)e(T)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6355
b(yp)l(es)26 b(and)f(Pr)l(o)l(gr)l(amming)h(L)l(anguages)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6356
Fw(,)f(c)n(hapter)d(Logical)663 2632 y(Relations)27 b(and)e(a)h(Case)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6357
(Study)c(in)i(Equiv)l(alence)g(Chec)n(king,)g(pages)h(223{244.)38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6358
b(MIT)27 b(Press,)663 2723 y(2005.)p Black 561 2814 a(5.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6359
Black 43 w(J.)e(Gallier.)35 b Fk(L)l(o)l(gic)28 b(for)e(Computer)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6360
(Scienc)l(e:)e(F)-6 b(oundations)28 b(of)f(A)n(utomatic)h(The)l(or)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6361
(em)g(Pr)l(ov-)663 2906 y(ing)p Fw(.)34 b(Harp)r(er)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6362
b(&)f(Ro)n(w,)h(1986.)p Black 561 2997 a(6.)p Black 43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6363
w(J.)32 b(McKinna)f(and)g(R.)g(P)n(ollac)n(k.)53 b(Some)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6364
b(t)n(yp)r(e)h(theory)g(and)g(lam)n(b)r(da)f(calculus)j(formalised.)663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6365
3088 y Fk(Journal)28 b(of)f(A)n(utomate)l(d)j(R)l(e)l(asoning)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6366
Fw(,)d(23\(1-4\),)g(1999.)p Black 561 3180 a(7.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6367
43 w(M.)32 b(Norrish.)54 b(Mec)n(hanising)33 b Fn(\025)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6368
Fw(-calculus)f(using)g(a)h(classical)h(\014rst)e(order)g(theory)g(of)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6369
(terms)663 3271 y(with)26 b(p)r(erm)n(utation.)33 b Fk(Higher-Or)l(der)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6370
d(and)e(Symb)l(olic)f(Computation)p Fw(,)g(19:169{195,)j(2006.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6371
Black 561 3362 a(8.)p Black 43 w(A.)25 b(M.)i(Pitts.)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6372
b(Nominal)25 b(Logic,)j(A)d(First)i(Order)e(Theory)h(of)h(Names)e(and)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6373
(Binding.)36 b Fk(Infor-)663 3454 y(mation)27 b(and)h(Computation)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6374
Fw(,)g(186:165{193,)i(2003.)p Black 561 3545 a(9.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6375
43 w(C.)39 b(Urban)e(and)h(S.)g(Berghofer.)73 b(A)38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6376
b(Recursion)g(Com)n(binator)g(for)h(Nominal)f(Datat)n(yp)r(es)663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6377
3636 y(Implemen)n(ted)22 b(in)j(Isab)r(elle/HOL.)35 b(In)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6378
b Fk(Pr)l(o)l(c.)i(of)g(the)h(3r)l(d)g(International)h(Joint)e(Confer)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6379
(enc)l(e)663 3728 y(on)g(A)n(utomate)l(d)j(R)l(e)l(asoning)e(\(IJCAR\))
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6380
p Fw(,)f(v)n(olume)d(4130)k(of)e Fk(LNAI)p Fw(,)g(pages)g(498{512,)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6381
(2006.)p Black 523 3819 a(10.)p Black 43 w(C.)22 b(Urban)f(and)h(M.)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6382
(Norrish.)29 b(A)21 b(formal)h(treatmen)n(t)f(of)i(the)e(Barendregt)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6383
(V)-6 b(ariable)23 b(Con)n(v)n(en-)663 3910 y(tion)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6384
b(in)h(rule)f(inductions.)43 b(In)28 b Fk(MERLIN)h('05:)h(Pr)l(o)l(c)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6385
(e)l(e)l(dings)i(of)e(the)h(3r)l(d)g(A)n(CM)f(SIGPLAN)663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6386
4002 y(workshop)36 b(on)g(Me)l(chanize)l(d)g(r)l(e)l(asoning)g(ab)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6387
(out)h(languages)f(with)f(variable)h(binding)p Fw(,)e(pages)663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6388
4093 y(25{32,)28 b(New)d(Y)-6 b(ork,)25 b(NY,)h(USA,)e(2005.)k(A)n(CM)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6389
(Press.)p Black 523 4184 a(11.)p Black 43 w(C.)32 b(Urban)f(and)g(C.)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6390
(T)-6 b(asson.)53 b(Nominal)31 b(tec)n(hniques)g(in)g(Isab)r(elle/HOL.)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6391
53 b(In)31 b Fk(Pr)l(o)l(c.)i(of)g(the)663 4276 y(20th)d(International)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6392
g(Confer)l(enc)l(e)g(on)f(A)n(utomate)l(d)i(De)l(duction)f(\(CADE\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6393
Fw(,)d(v)n(olume)f(3632)j(of)663 4367 y Fk(L)l(e)l(ctur)l(e)g(Notes)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6394
(in)e(Computer)i(Scienc)l(e)p Fw(,)e(pages)f(38{53,)i(2005.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6395
Black 523 4458 a(12.)p Black 43 w(M.)d(W)-6 b(enzel.)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6396
b(Isar)25 b(|)g(A)g(Generic)h(In)n(terpretativ)n(e)e(Approac)n(h)g(to)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6397
(Readable)f(Formal)g(Pro)r(of)663 4550 y(Do)r(cumen)n(ts.)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6398
b(In)24 b Fk(Pr)l(o)l(c.)j(of)e(the)j(12th)f(International)g(Confer)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6399
(enc)l(e)h(on)e(The)l(or)l(em)h(Pr)l(oving)g(in)663 4641
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6400
y(Higher)h(Or)l(der)g(L)l(o)l(gics)h(\(TPHOLs\))p Fw(,)e(n)n(um)n(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6401
(er)c(1690)k(in)f(LNCS,)g(pages)g(167{184,)j(1999.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6402
Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6403
%%Trailer
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6404
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6405
userdict /end-hook known{end-hook}if
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6406
%%EOF