--- a/src/HOL/Nominal/Nominal.thy Mon Sep 05 14:42:31 2011 +0200
+++ b/src/HOL/Nominal/Nominal.thy Mon Sep 05 22:02:32 2011 +0200
@@ -51,16 +51,16 @@
begin
definition
- perm_fun_def: "perm_fun pi (f::'a\<Rightarrow>'b) = (\<lambda>x. pi\<bullet>f((rev pi)\<bullet>x))"
+ "perm_fun pi f = (\<lambda>x. pi \<bullet> f (rev pi \<bullet> x))"
definition perm_bool :: "'x prm \<Rightarrow> bool \<Rightarrow> bool" where
- perm_bool_def: "perm_bool pi b = b"
+ "perm_bool pi b = b"
primrec perm_unit :: "'x prm \<Rightarrow> unit \<Rightarrow> unit" where
"perm_unit pi () = ()"
primrec perm_prod :: "'x prm \<Rightarrow> ('a\<times>'b) \<Rightarrow> ('a\<times>'b)" where
- "perm_prod pi (x,y) = (pi\<bullet>x,pi\<bullet>y)"
+ "perm_prod pi (x, y) = (pi\<bullet>x, pi\<bullet>y)"
primrec perm_list :: "'x prm \<Rightarrow> 'a list \<Rightarrow> 'a list" where
nil_eqvt: "perm_list pi [] = []"
@@ -71,13 +71,13 @@
| none_eqvt: "perm_option pi None = None"
definition perm_char :: "'x prm \<Rightarrow> char \<Rightarrow> char" where
- perm_char_def: "perm_char pi c = c"
+ "perm_char pi c = c"
definition perm_nat :: "'x prm \<Rightarrow> nat \<Rightarrow> nat" where
- perm_nat_def: "perm_nat pi i = i"
+ "perm_nat pi i = i"
definition perm_int :: "'x prm \<Rightarrow> int \<Rightarrow> int" where
- perm_int_def: "perm_int pi i = i"
+ "perm_int pi i = i"
primrec perm_noption :: "'x prm \<Rightarrow> 'a noption \<Rightarrow> 'a noption" where
nsome_eqvt: "perm_noption pi (nSome x) = nSome (pi\<bullet>x)"
@@ -962,7 +962,7 @@
fixes pi::"'y prm"
and x ::"'x set"
assumes dj: "disjoint TYPE('x) TYPE('y)"
- shows "(pi\<bullet>x)=x"
+ shows "pi\<bullet>x=x"
using dj by (simp_all add: perm_fun_def disjoint_def perm_bool)
lemma dj_perm_perm_forget:
@@ -1028,7 +1028,7 @@
qed
lemma pt_unit_inst:
- shows "pt TYPE(unit) TYPE('x)"
+ shows "pt TYPE(unit) TYPE('x)"
by (simp add: pt_def)
lemma pt_prod_inst: