author | wenzelm |
Wed, 10 Oct 2012 15:21:26 +0200 | |
changeset 49754 | acafcac41690 |
parent 48174 | eb72f99737be |
child 49762 | b5e355c41de3 |
permissions | -rw-r--r-- |
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(* Title: HOL/ex/Set_Comprehension_Pointfree_Tests.thy |
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Improved tactic for rewriting set comprehensions into pointfree form.
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Author: Lukas Bulwahn, Rafal Kolanski |
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Copyright 2012 TU Muenchen |
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*) |
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header {* Tests for the set comprehension to pointfree simproc *} |
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theory Set_Comprehension_Pointfree_Tests |
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imports Main |
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begin |
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|
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parents:
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lemma |
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Improved tactic for rewriting set comprehensions into pointfree form.
Rafal Kolanski <rafal.kolanski@nicta.com.au>
parents:
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"finite {p. EX x. p = (x, x)}" |
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Improved tactic for rewriting set comprehensions into pointfree form.
Rafal Kolanski <rafal.kolanski@nicta.com.au>
parents:
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apply simp |
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Improved tactic for rewriting set comprehensions into pointfree form.
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parents:
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oops |
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lemma |
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"finite {f a b| a b. a : A \<and> b : B}" |
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apply simp |
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Improved tactic for rewriting set comprehensions into pointfree form.
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oops |
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lemma |
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"finite {f a b| a b. a : A \<and> a : A' \<and> b : B}" |
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apply simp |
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parents:
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oops |
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lemma |
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"finite {f a b| a b. a : A \<and> b : B \<and> b : B'}" |
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apply simp |
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parents:
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oops |
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lemma |
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"finite {f a b c| a b c. a : A \<and> b : B \<and> c : C}" |
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apply simp |
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parents:
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oops |
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lemma |
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"finite {f a b c d| a b c d. a : A \<and> b : B \<and> c : C \<and> d : D}" |
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parents:
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apply simp |
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parents:
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oops |
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lemma |
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"finite {f a b c d e | a b c d e. a : A \<and> b : B \<and> c : C \<and> d : D \<and> e : E}" |
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parents:
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apply simp |
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parents:
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oops |
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Rafal Kolanski <rafal.kolanski@nicta.com.au>
parents:
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|
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parents:
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lemma (* check arbitrary ordering *) |
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parents:
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"finite {f a d c b e | e b c d a. b : B \<and> a : A \<and> e : E' \<and> c : C \<and> d : D \<and> e : E \<and> b : B'}" |
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parents:
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apply simp |
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parents:
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oops |
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parents:
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|
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parents:
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lemma |
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parents:
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"\<lbrakk> finite A ; finite B ; finite C ; finite D \<rbrakk> |
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\<Longrightarrow> finite ({f a b c d| a b c d. a : A \<and> b : B \<and> c : C \<and> d : D})" |
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by simp |
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|
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lemma |
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"finite ((\<lambda>(a,b,c,d). f a b c d) ` (A \<times> B \<times> C \<times> D)) |
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parents:
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\<Longrightarrow> finite ({f a b c d| a b c d. a : A \<and> b : B \<and> c : C \<and> d : D})" |
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parents:
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by simp |
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parents:
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|
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schematic_lemma (* check interaction with schematics *) |
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"finite {x :: ?'A \<Rightarrow> ?'B \<Rightarrow> bool. \<exists>a b. x = Pair_Rep a b} |
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= finite ((\<lambda>(a:: ?'A, b :: ?'B). Pair_Rep a b) ` (UNIV \<times> UNIV))" |
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parents:
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by simp |
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lemma |
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assumes "finite S" shows "finite {(a,b,c,d). ([a, b], [c, d]) : S}" |
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proof - |
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have eq: "{(a,b,c,d). ([a, b], [c, d]) : S} = ((%(a, b, c, d). ([a, b], [c, d])) -` S)" |
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unfolding vimage_def by (auto split: prod.split) (* to be proved with the simproc *) |
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from `finite S` show ?thesis |
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unfolding eq by (auto intro!: finite_vimageI simp add: inj_on_def) |
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(* to be automated with further rules and automation *) |
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qed |
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end |