| author | Christian Urban <christian dot urban at kcl dot ac dot uk> |
| Thu, 06 Dec 2012 15:11:21 +0000 | |
| changeset 0 | 110247f9d47e |
| child 33 | 9b9f2117561f |
| permissions | -rw-r--r-- |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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header {* Order on product types *}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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theory Precedence_ord |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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imports Main |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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begin |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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datatype precedence = Prc nat nat |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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instantiation precedence :: order |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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begin |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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definition |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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precedence_le_def: "x \<le> y \<longleftrightarrow> (case (x, y) of |
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(Prc fx sx, Prc fy sy) \<Rightarrow> |
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fx < fy \<or> (fx \<le> fy \<and> sy \<le> sx))" |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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definition |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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precedence_less_def: "x < y \<longleftrightarrow> (case (x, y) of |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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(Prc fx sx, Prc fy sy) \<Rightarrow> |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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fx < fy \<or> (fx \<le> fy \<and> sy < sx))" |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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instance |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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proof |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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qed (auto simp: precedence_le_def precedence_less_def |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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intro: order_trans split:precedence.splits) |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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end |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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instance precedence :: preorder .. |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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instance precedence :: linorder proof |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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qed (auto simp: precedence_le_def precedence_less_def |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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intro: order_trans split:precedence.splits) |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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end |