src/HOL/Lifting_Sum.thy
 changeset 55943 5c2df04e97d1 parent 55931 62156e694f3d child 55945 e96383acecf9
```--- a/src/HOL/Lifting_Sum.thy	Thu Mar 06 15:14:09 2014 +0100
+++ b/src/HOL/Lifting_Sum.thy	Thu Mar 06 15:25:21 2014 +0100
@@ -12,54 +12,54 @@

abbreviation (input) "sum_pred \<equiv> case_sum"

-lemmas sum_rel_eq[relator_eq] = sum.rel_eq
-lemmas sum_rel_mono[relator_mono] = sum.rel_mono
+lemmas rel_sum_eq[relator_eq] = sum.rel_eq
+lemmas rel_sum_mono[relator_mono] = sum.rel_mono

-lemma sum_rel_OO[relator_distr]:
-  "(sum_rel A B) OO (sum_rel C D) = sum_rel (A OO C) (B OO D)"
-  by (rule ext)+ (auto simp add: sum_rel_def OO_def split_sum_ex split: sum.split)
+lemma rel_sum_OO[relator_distr]:
+  "(rel_sum A B) OO (rel_sum C D) = rel_sum (A OO C) (B OO D)"
+  by (rule ext)+ (auto simp add: rel_sum_def OO_def split_sum_ex split: sum.split)

lemma Domainp_sum[relator_domain]:
assumes "Domainp R1 = P1"
assumes "Domainp R2 = P2"
-  shows "Domainp (sum_rel R1 R2) = (sum_pred P1 P2)"
+  shows "Domainp (rel_sum R1 R2) = (sum_pred P1 P2)"
using assms
by (auto simp add: Domainp_iff split_sum_ex iff: fun_eq_iff split: sum.split)

-lemma left_total_sum_rel[reflexivity_rule]:
-  "left_total R1 \<Longrightarrow> left_total R2 \<Longrightarrow> left_total (sum_rel R1 R2)"
+lemma left_total_rel_sum[reflexivity_rule]:
+  "left_total R1 \<Longrightarrow> left_total R2 \<Longrightarrow> left_total (rel_sum R1 R2)"
using assms unfolding left_total_def split_sum_all split_sum_ex by simp

-lemma left_unique_sum_rel [reflexivity_rule]:
-  "left_unique R1 \<Longrightarrow> left_unique R2 \<Longrightarrow> left_unique (sum_rel R1 R2)"
+lemma left_unique_rel_sum [reflexivity_rule]:
+  "left_unique R1 \<Longrightarrow> left_unique R2 \<Longrightarrow> left_unique (rel_sum R1 R2)"
using assms unfolding left_unique_def split_sum_all by simp

-lemma right_total_sum_rel [transfer_rule]:
-  "right_total R1 \<Longrightarrow> right_total R2 \<Longrightarrow> right_total (sum_rel R1 R2)"
+lemma right_total_rel_sum [transfer_rule]:
+  "right_total R1 \<Longrightarrow> right_total R2 \<Longrightarrow> right_total (rel_sum R1 R2)"
unfolding right_total_def split_sum_all split_sum_ex by simp

-lemma right_unique_sum_rel [transfer_rule]:
-  "right_unique R1 \<Longrightarrow> right_unique R2 \<Longrightarrow> right_unique (sum_rel R1 R2)"
+lemma right_unique_rel_sum [transfer_rule]:
+  "right_unique R1 \<Longrightarrow> right_unique R2 \<Longrightarrow> right_unique (rel_sum R1 R2)"
unfolding right_unique_def split_sum_all by simp

-lemma bi_total_sum_rel [transfer_rule]:
-  "bi_total R1 \<Longrightarrow> bi_total R2 \<Longrightarrow> bi_total (sum_rel R1 R2)"
+lemma bi_total_rel_sum [transfer_rule]:
+  "bi_total R1 \<Longrightarrow> bi_total R2 \<Longrightarrow> bi_total (rel_sum R1 R2)"
using assms unfolding bi_total_def split_sum_all split_sum_ex by simp

-lemma bi_unique_sum_rel [transfer_rule]:
-  "bi_unique R1 \<Longrightarrow> bi_unique R2 \<Longrightarrow> bi_unique (sum_rel R1 R2)"
+lemma bi_unique_rel_sum [transfer_rule]:
+  "bi_unique R1 \<Longrightarrow> bi_unique R2 \<Longrightarrow> bi_unique (rel_sum R1 R2)"
using assms unfolding bi_unique_def split_sum_all by simp

lemma sum_invariant_commute [invariant_commute]:
-  "sum_rel (Lifting.invariant P1) (Lifting.invariant P2) = Lifting.invariant (sum_pred P1 P2)"
-  by (auto simp add: fun_eq_iff Lifting.invariant_def sum_rel_def split: sum.split)
+  "rel_sum (Lifting.invariant P1) (Lifting.invariant P2) = Lifting.invariant (sum_pred P1 P2)"
+  by (auto simp add: fun_eq_iff Lifting.invariant_def rel_sum_def split: sum.split)

subsection {* Quotient theorem for the Lifting package *}

lemma Quotient_sum[quot_map]:
assumes "Quotient R1 Abs1 Rep1 T1"
assumes "Quotient R2 Abs2 Rep2 T2"
-  shows "Quotient (sum_rel R1 R2) (map_sum Abs1 Abs2) (map_sum Rep1 Rep2) (sum_rel T1 T2)"
+  shows "Quotient (rel_sum R1 R2) (map_sum Abs1 Abs2) (map_sum Rep1 Rep2) (rel_sum T1 T2)"
using assms unfolding Quotient_alt_def

@@ -69,15 +69,15 @@
begin
interpretation lifting_syntax .

-lemma Inl_transfer [transfer_rule]: "(A ===> sum_rel A B) Inl Inl"
+lemma Inl_transfer [transfer_rule]: "(A ===> rel_sum A B) Inl Inl"
unfolding fun_rel_def by simp

-lemma Inr_transfer [transfer_rule]: "(B ===> sum_rel A B) Inr Inr"
+lemma Inr_transfer [transfer_rule]: "(B ===> rel_sum A B) Inr Inr"
unfolding fun_rel_def by simp

lemma case_sum_transfer [transfer_rule]:
-  "((A ===> C) ===> (B ===> C) ===> sum_rel A B ===> C) case_sum case_sum"
-  unfolding fun_rel_def sum_rel_def by (simp split: sum.split)
+  "((A ===> C) ===> (B ===> C) ===> rel_sum A B ===> C) case_sum case_sum"
+  unfolding fun_rel_def rel_sum_def by (simp split: sum.split)

end
```