author | Cezary Kaliszyk <kaliszyk@in.tum.de> |
Fri, 19 Feb 2010 13:54:19 +0100 | |
changeset 35222 | 4f1fba00f66d |
child 35788 | f1deaca15ca3 |
permissions | -rw-r--r-- |
35222
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
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(* Title: Quotient_Option.thy |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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Author: Cezary Kaliszyk and Christian Urban |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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*) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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theory Quotient_Option |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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imports Main Quotient_Syntax |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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begin |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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section {* Quotient infrastructure for the option type. *} |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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fun |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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option_rel |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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where |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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"option_rel R None None = True" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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| "option_rel R (Some x) None = False" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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| "option_rel R None (Some x) = False" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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| "option_rel R (Some x) (Some y) = R x y" |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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declare [[map option = (Option.map, option_rel)]] |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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text {* should probably be in Option.thy *} |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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lemma split_option_all: |
4f1fba00f66d
Initial version of HOL quotient package.
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shows "(\<forall>x. P x) \<longleftrightarrow> P None \<and> (\<forall>a. P (Some a))" |
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Initial version of HOL quotient package.
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parents:
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apply(auto) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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apply(case_tac x) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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apply(simp_all) |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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done |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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|
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Initial version of HOL quotient package.
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parents:
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lemma option_quotient[quot_thm]: |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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assumes q: "Quotient R Abs Rep" |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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shows "Quotient (option_rel R) (Option.map Abs) (Option.map Rep)" |
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Initial version of HOL quotient package.
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parents:
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unfolding Quotient_def |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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apply(simp add: split_option_all) |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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apply(simp add: Quotient_abs_rep[OF q] Quotient_rel_rep[OF q]) |
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Initial version of HOL quotient package.
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using q |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
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unfolding Quotient_def |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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apply(blast) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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done |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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lemma option_equivp[quot_equiv]: |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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assumes a: "equivp R" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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shows "equivp (option_rel R)" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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apply(rule equivpI) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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unfolding reflp_def symp_def transp_def |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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apply(simp_all add: split_option_all) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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apply(blast intro: equivp_reflp[OF a]) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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apply(blast intro: equivp_symp[OF a]) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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apply(blast intro: equivp_transp[OF a]) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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done |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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|
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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lemma option_None_rsp[quot_respect]: |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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assumes q: "Quotient R Abs Rep" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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shows "option_rel R None None" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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by simp |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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|
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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lemma option_Some_rsp[quot_respect]: |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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assumes q: "Quotient R Abs Rep" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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shows "(R ===> option_rel R) Some Some" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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by simp |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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lemma option_None_prs[quot_preserve]: |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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assumes q: "Quotient R Abs Rep" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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shows "Option.map Abs None = None" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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by simp |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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lemma option_Some_prs[quot_preserve]: |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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assumes q: "Quotient R Abs Rep" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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shows "(Rep ---> Option.map Abs) Some = Some" |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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apply(simp add: expand_fun_eq) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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apply(simp add: Quotient_abs_rep[OF q]) |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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done |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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lemma option_map_id[id_simps]: |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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shows "Option.map id = id" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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by (simp add: expand_fun_eq split_option_all) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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lemma option_rel_eq[id_simps]: |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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shows "option_rel (op =) = (op =)" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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78 |
by (simp add: expand_fun_eq split_option_all) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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|
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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end |