src/HOL/Library/Quotient_Sum.thy
changeset 53026 e1a548c11845
parent 53012 cb82606b8215
child 55564 e81ee43ab290
     1.1 --- a/src/HOL/Library/Quotient_Sum.thy	Wed Aug 14 00:15:03 2013 +0200
     1.2 +++ b/src/HOL/Library/Quotient_Sum.thy	Tue Aug 13 18:22:55 2013 +0200
     1.3 @@ -12,11 +12,11 @@
     1.4  
     1.5  lemma sum_rel_map1:
     1.6    "sum_rel R1 R2 (sum_map f1 f2 x) y \<longleftrightarrow> sum_rel (\<lambda>x. R1 (f1 x)) (\<lambda>x. R2 (f2 x)) x y"
     1.7 -  by (simp add: sum_rel_unfold split: sum.split)
     1.8 +  by (simp add: sum_rel_def split: sum.split)
     1.9  
    1.10  lemma sum_rel_map2:
    1.11    "sum_rel R1 R2 x (sum_map f1 f2 y) \<longleftrightarrow> sum_rel (\<lambda>x y. R1 x (f1 y)) (\<lambda>x y. R2 x (f2 y)) x y"
    1.12 -  by (simp add: sum_rel_unfold split: sum.split)
    1.13 +  by (simp add: sum_rel_def split: sum.split)
    1.14  
    1.15  lemma sum_map_id [id_simps]:
    1.16    "sum_map id id = id"
    1.17 @@ -24,15 +24,15 @@
    1.18  
    1.19  lemma sum_rel_eq [id_simps]:
    1.20    "sum_rel (op =) (op =) = (op =)"
    1.21 -  by (simp add: sum_rel_unfold fun_eq_iff split: sum.split)
    1.22 +  by (simp add: sum_rel_def fun_eq_iff split: sum.split)
    1.23  
    1.24  lemma sum_symp:
    1.25    "symp R1 \<Longrightarrow> symp R2 \<Longrightarrow> symp (sum_rel R1 R2)"
    1.26 -  unfolding symp_def split_sum_all sum_rel.simps by fast
    1.27 +  unfolding symp_def split_sum_all sum_rel_simps by fast
    1.28  
    1.29  lemma sum_transp:
    1.30    "transp R1 \<Longrightarrow> transp R2 \<Longrightarrow> transp (sum_rel R1 R2)"
    1.31 -  unfolding transp_def split_sum_all sum_rel.simps by fast
    1.32 +  unfolding transp_def split_sum_all sum_rel_simps by fast
    1.33  
    1.34  lemma sum_equivp [quot_equiv]:
    1.35    "equivp R1 \<Longrightarrow> equivp R2 \<Longrightarrow> equivp (sum_rel R1 R2)"
    1.36 @@ -46,7 +46,7 @@
    1.37    apply (simp_all add: sum_map.compositionality comp_def sum_map.identity sum_rel_eq sum_rel_map1 sum_rel_map2
    1.38      Quotient3_abs_rep [OF q1] Quotient3_rel_rep [OF q1] Quotient3_abs_rep [OF q2] Quotient3_rel_rep [OF q2])
    1.39    using Quotient3_rel [OF q1] Quotient3_rel [OF q2]
    1.40 -  apply (simp add: sum_rel_unfold comp_def split: sum.split)
    1.41 +  apply (simp add: sum_rel_def comp_def split: sum.split)
    1.42    done
    1.43  
    1.44  declare [[mapQ3 sum = (sum_rel, sum_quotient)]]