--- a/src/HOL/Library/Quotient_Sum.thy Fri Nov 07 12:24:56 2014 +0100
+++ b/src/HOL/Library/Quotient_Sum.thy Fri Nov 07 11:28:37 2014 +0100
@@ -12,11 +12,11 @@
lemma rel_sum_map1:
"rel_sum R1 R2 (map_sum f1 f2 x) y \<longleftrightarrow> rel_sum (\<lambda>x. R1 (f1 x)) (\<lambda>x. R2 (f2 x)) x y"
- by (simp add: rel_sum_def split: sum.split)
+ by (rule sum.rel_map(1))
lemma rel_sum_map2:
"rel_sum R1 R2 x (map_sum f1 f2 y) \<longleftrightarrow> rel_sum (\<lambda>x y. R1 x (f1 y)) (\<lambda>x y. R2 x (f2 y)) x y"
- by (simp add: rel_sum_def split: sum.split)
+ by (rule sum.rel_map(2))
lemma map_sum_id [id_simps]:
"map_sum id id = id"
@@ -24,7 +24,7 @@
lemma rel_sum_eq [id_simps]:
"rel_sum (op =) (op =) = (op =)"
- by (simp add: rel_sum_def fun_eq_iff split: sum.split)
+ by (rule sum.rel_eq)
lemma reflp_rel_sum:
"reflp R1 \<Longrightarrow> reflp R2 \<Longrightarrow> reflp (rel_sum R1 R2)"
@@ -50,7 +50,7 @@
apply (simp_all add: map_sum.compositionality comp_def map_sum.identity rel_sum_eq rel_sum_map1 rel_sum_map2
Quotient3_abs_rep [OF q1] Quotient3_rel_rep [OF q1] Quotient3_abs_rep [OF q2] Quotient3_rel_rep [OF q2])
using Quotient3_rel [OF q1] Quotient3_rel [OF q2]
- apply (simp add: rel_sum_def comp_def split: sum.split)
+ apply (fastforce elim!: rel_sum.cases simp add: comp_def split: sum.split)
done
declare [[mapQ3 sum = (rel_sum, sum_quotient)]]