author | bulwahn |
Mon, 22 Nov 2010 11:34:56 +0100 | |
changeset 40650 | d40b347d5b0b |
parent 40610 | 70776ecfe324 |
child 40820 | fd9c98ead9a9 |
permissions | -rw-r--r-- |
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(* Title: HOL/Library/Quotient_Sum.thy |
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Initial version of HOL quotient package.
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Author: Cezary Kaliszyk and Christian Urban |
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Initial version of HOL quotient package.
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*) |
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header {* Quotient infrastructure for the sum type *} |
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||
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Initial version of HOL quotient package.
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theory Quotient_Sum |
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Initial version of HOL quotient package.
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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 |
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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re-generalized type of option_rel and sum_rel (accident from 2989f9f3aa10)
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sum_rel :: "('a \<Rightarrow> 'c \<Rightarrow> bool) \<Rightarrow> ('b \<Rightarrow> 'd \<Rightarrow> bool) \<Rightarrow> 'a + 'b \<Rightarrow> 'c + 'd \<Rightarrow> bool" |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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where |
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Initial version of HOL quotient package.
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parents:
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"sum_rel R1 R2 (Inl a1) (Inl b1) = R1 a1 b1" |
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Initial version of HOL quotient package.
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parents:
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| "sum_rel R1 R2 (Inl a1) (Inr b2) = False" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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| "sum_rel R1 R2 (Inr a2) (Inl b1) = False" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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| "sum_rel R1 R2 (Inr a2) (Inr b2) = R2 a2 b2" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
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0040bafffdef
"prod" and "sum" replace "*" and "+" respectively
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declare [[map sum = (sum_map, sum_rel)]] |
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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:
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text {* should probably be in @{theory Sum_Type} *} |
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Initial version of HOL quotient package.
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parents:
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lemma split_sum_all: |
4f1fba00f66d
Initial version of HOL quotient package.
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shows "(\<forall>x. P x) \<longleftrightarrow> (\<forall>x. P (Inl x)) \<and> (\<forall>x. P (Inr x))" |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
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.
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apply(simp_all) |
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Initial version of HOL quotient package.
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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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lemma sum_equivp[quot_equiv]: |
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Initial version of HOL quotient package.
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assumes a: "equivp R1" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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assumes b: "equivp R2" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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shows "equivp (sum_rel R1 R2)" |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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apply(rule equivpI) |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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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:
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apply(simp_all add: split_sum_all) |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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apply(blast intro: equivp_reflp[OF a] equivp_reflp[OF b]) |
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] equivp_symp[OF b]) |
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] equivp_transp[OF b]) |
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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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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lemma sum_quotient[quot_thm]: |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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assumes q1: "Quotient R1 Abs1 Rep1" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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assumes q2: "Quotient R2 Abs2 Rep2" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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shows "Quotient (sum_rel R1 R2) (sum_map Abs1 Abs2) (sum_map Rep1 Rep2)" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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unfolding Quotient_def |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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apply(simp add: split_sum_all) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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apply(simp_all add: Quotient_abs_rep[OF q1] Quotient_rel_rep[OF q1]) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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apply(simp_all add: Quotient_abs_rep[OF q2] Quotient_rel_rep[OF q2]) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
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using q1 q2 |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
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(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
changeset
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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lemma sum_Inl_rsp[quot_respect]: |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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assumes q1: "Quotient R1 Abs1 Rep1" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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assumes q2: "Quotient R2 Abs2 Rep2" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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shows "(R1 ===> sum_rel R1 R2) Inl Inl" |
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more appropriate specification packages; fun_rel_def is no simp rule by default
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by auto |
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Initial version of HOL quotient package.
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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lemma sum_Inr_rsp[quot_respect]: |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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assumes q1: "Quotient R1 Abs1 Rep1" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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assumes q2: "Quotient R2 Abs2 Rep2" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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shows "(R2 ===> sum_rel R1 R2) Inr Inr" |
40465
2989f9f3aa10
more appropriate specification packages; fun_rel_def is no simp rule by default
haftmann
parents:
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by auto |
35222
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.
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parents:
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lemma sum_Inl_prs[quot_preserve]: |
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Initial version of HOL quotient package.
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assumes q1: "Quotient R1 Abs1 Rep1" |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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assumes q2: "Quotient R2 Abs2 Rep2" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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shows "(Rep1 ---> sum_map Abs1 Abs2) Inl = Inl" |
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renamed lemmas: ext_iff -> fun_eq_iff, set_ext_iff -> set_eq_iff, set_ext -> set_eqI
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apply(simp add: fun_eq_iff) |
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Initial version of HOL quotient package.
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parents:
diff
changeset
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apply(simp add: Quotient_abs_rep[OF q1]) |
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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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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lemma sum_Inr_prs[quot_preserve]: |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
diff
changeset
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assumes q1: "Quotient R1 Abs1 Rep1" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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assumes q2: "Quotient R2 Abs2 Rep2" |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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shows "(Rep2 ---> sum_map Abs1 Abs2) Inr = Inr" |
39302
d7728f65b353
renamed lemmas: ext_iff -> fun_eq_iff, set_ext_iff -> set_eq_iff, set_ext -> set_eqI
nipkow
parents:
39198
diff
changeset
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apply(simp add: fun_eq_iff) |
35222
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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 q2]) |
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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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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lemma sum_map_id[id_simps]: |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
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shows "sum_map id id = id" |
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renamed lemmas: ext_iff -> fun_eq_iff, set_ext_iff -> set_eq_iff, set_ext -> set_eqI
nipkow
parents:
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changeset
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by (simp add: fun_eq_iff split_sum_all) |
35222
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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
changeset
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lemma sum_rel_eq[id_simps]: |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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shows "sum_rel (op =) (op =) = (op =)" |
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d7728f65b353
renamed lemmas: ext_iff -> fun_eq_iff, set_ext_iff -> set_eq_iff, set_ext -> set_eqI
nipkow
parents:
39198
diff
changeset
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by (simp add: fun_eq_iff split_sum_all) |
35222
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:
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end |