src/HOL/Quotient.thy
 changeset 39956 132b79985660 parent 39946 78faa9b31202 child 40031 2671cce4d25d
```     1.1 --- a/src/HOL/Quotient.thy	Tue Oct 05 12:04:49 2010 +0200
1.2 +++ b/src/HOL/Quotient.thy	Tue Oct 05 12:04:57 2010 +0200
1.3 @@ -319,12 +319,12 @@
1.4  lemma ball_reg_right:
1.5    assumes a: "\<And>x. R x \<Longrightarrow> P x \<longrightarrow> Q x"
1.6    shows "All P \<longrightarrow> Ball R Q"
1.7 -  using a by (metis COMBC_def Collect_def Collect_mem_eq)
1.8 +  using a by (metis Collect_def Collect_mem_eq)
1.9
1.10  lemma bex_reg_left:
1.11    assumes a: "\<And>x. R x \<Longrightarrow> Q x \<longrightarrow> P x"
1.12    shows "Bex R Q \<longrightarrow> Ex P"
1.13 -  using a by (metis COMBC_def Collect_def Collect_mem_eq)
1.14 +  using a by (metis Collect_def Collect_mem_eq)
1.15
1.16  lemma ball_reg_left:
1.17    assumes a: "equivp R"
1.18 @@ -381,13 +381,13 @@
1.19    assumes a: "!x :: 'a. (R x --> P x --> Q x)"
1.20    and     b: "Ball R P"
1.21    shows "Ball R Q"
1.22 -  using a b by (metis COMBC_def Collect_def Collect_mem_eq)
1.23 +  using a b by (metis Collect_def Collect_mem_eq)
1.24
1.25  lemma bex_reg:
1.26    assumes a: "!x :: 'a. (R x --> P x --> Q x)"
1.27    and     b: "Bex R P"
1.28    shows "Bex R Q"
1.29 -  using a b by (metis COMBC_def Collect_def Collect_mem_eq)
1.30 +  using a b by (metis Collect_def Collect_mem_eq)
1.31
1.32
1.33  lemma ball_all_comm:
```