| author | Cezary Kaliszyk <kaliszyk@in.tum.de> |
| Fri, 19 Aug 2011 11:01:52 +0900 | |
| changeset 2995 | 6d2859aeebba |
| parent 2950 | 0911cb7bf696 |
| permissions | -rw-r--r-- |
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theory Foo1 |
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imports "../Nominal2" |
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begin |
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text {*
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Contrived example that has more than one |
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binding function |
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*} |
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proved that bn functions return a finite set
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atom_decl name |
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nominal_datatype foo: trm = |
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Var "name" |
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| App "trm" "trm" |
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| Lam x::"name" t::"trm" binds x in t |
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0911cb7bf696
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| Let1 a::"assg" t::"trm" binds "bn1 a" in t |
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0911cb7bf696
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parents:
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| Let2 a::"assg" t::"trm" binds "bn2 a" in t |
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0911cb7bf696
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parents:
2630
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| Let3 a::"assg" t::"trm" binds "bn3 a" in t |
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| Let4 a::"assg'" t::"trm" binds (set) "bn4 a" in t |
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and assg = |
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As "name" "name" "trm" |
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and assg' = |
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BNil |
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| BAs "name" "assg'" |
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binder |
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bn1::"assg \<Rightarrow> atom list" and |
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bn2::"assg \<Rightarrow> atom list" and |
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bn3::"assg \<Rightarrow> atom list" and |
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bn4::"assg' \<Rightarrow> atom set" |
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where |
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"bn1 (As x y t) = [atom x]" |
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| "bn2 (As x y t) = [atom y]" |
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| "bn3 (As x y t) = [atom x, atom y]" |
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| "bn4 (BNil) = {}"
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| "bn4 (BAs a as) = {atom a} \<union> bn4 as"
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thm foo.permute_bn |
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thm foo.perm_bn_alpha |
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thm foo.perm_bn_simps |
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thm foo.bn_finite |
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thm foo.distinct |
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thm foo.induct |
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thm foo.inducts |
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thm foo.exhaust |
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thm foo.strong_induct |
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thm foo.strong_exhaust |
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thm foo.fv_defs |
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thm foo.bn_defs |
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thm foo.perm_simps |
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thm foo.eq_iff |
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thm foo.fv_bn_eqvt |
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thm foo.size_eqvt |
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thm foo.supports |
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thm foo.fsupp |
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thm foo.supp |
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thm foo.fresh |
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f0252365936c
proved that bn functions return a finite set
Christian Urban <urbanc@in.tum.de>
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thm foo.bn_finite |
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end |
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