
diff -r af95a414136a -r 6abda9b6b9c1 src/HOL/SMT2.thy
--- a/src/HOL/SMT2.thy	Tue Jun 03 16:02:41 2014 +0200
+++ b/src/HOL/SMT2.thy	Tue Jun 03 16:02:42 2014 +0200
@@ -298,20 +298,20 @@
   if_True if_False not_not
 
 lemma [z3_new_rule]:
-  "(P \<and> Q) = (\<not>(\<not>P \<or> \<not>Q))"
-  "(P \<and> Q) = (\<not>(\<not>Q \<or> \<not>P))"
-  "(\<not>P \<and> Q) = (\<not>(P \<or> \<not>Q))"
-  "(\<not>P \<and> Q) = (\<not>(\<not>Q \<or> P))"
-  "(P \<and> \<not>Q) = (\<not>(\<not>P \<or> Q))"
-  "(P \<and> \<not>Q) = (\<not>(Q \<or> \<not>P))"
-  "(\<not>P \<and> \<not>Q) = (\<not>(P \<or> Q))"
-  "(\<not>P \<and> \<not>Q) = (\<not>(Q \<or> P))"
+  "(P \<and> Q) = (\<not> (\<not> P \<or> \<not> Q))"
+  "(P \<and> Q) = (\<not> (\<not> Q \<or> \<not> P))"
+  "(\<not> P \<and> Q) = (\<not> (P \<or> \<not> Q))"
+  "(\<not> P \<and> Q) = (\<not> (\<not> Q \<or> P))"
+  "(P \<and> \<not> Q) = (\<not> (\<not> P \<or> Q))"
+  "(P \<and> \<not> Q) = (\<not> (Q \<or> \<not> P))"
+  "(\<not> P \<and> \<not> Q) = (\<not> (P \<or> Q))"
+  "(\<not> P \<and> \<not> Q) = (\<not> (Q \<or> P))"
   by auto
 
 lemma [z3_new_rule]:
-  "(P \<longrightarrow> Q) = (Q \<or> \<not>P)"
-  "(\<not>P \<longrightarrow> Q) = (P \<or> Q)"
-  "(\<not>P \<longrightarrow> Q) = (Q \<or> P)"
+  "(P \<longrightarrow> Q) = (Q \<or> \<not> P)"
+  "(\<not> P \<longrightarrow> Q) = (P \<or> Q)"
+  "(\<not> P \<longrightarrow> Q) = (Q \<or> P)"
   "(True \<longrightarrow> P) = P"
   "(P \<longrightarrow> True) = True"
   "(False \<longrightarrow> P) = True"
@@ -319,41 +319,41 @@
   by auto
 
 lemma [z3_new_rule]:
-  "((P = Q) \<longrightarrow> R) = (R | (Q = (\<not>P)))"
+  "((P = Q) \<longrightarrow> R) = (R | (Q = (\<not> P)))"
   by auto
 
 lemma [z3_new_rule]:
-  "(\<not>True) = False"
-  "(\<not>False) = True"
+  "(\<not> True) = False"
+  "(\<not> False) = True"
   "(x = x) = True"
   "(P = True) = P"
   "(True = P) = P"
-  "(P = False) = (\<not>P)"
-  "(False = P) = (\<not>P)"
-  "((\<not>P) = P) = False"
-  "(P = (\<not>P)) = False"
-  "((\<not>P) = (\<not>Q)) = (P = Q)"
-  "\<not>(P = (\<not>Q)) = (P = Q)"
-  "\<not>((\<not>P) = Q) = (P = Q)"
-  "(P \<noteq> Q) = (Q = (\<not>P))"
-  "(P = Q) = ((\<not>P \<or> Q) \<and> (P \<or> \<not>Q))"
-  "(P \<noteq> Q) = ((\<not>P \<or> \<not>Q) \<and> (P \<or> Q))"
+  "(P = False) = (\<not> P)"
+  "(False = P) = (\<not> P)"
+  "((\<not> P) = P) = False"
+  "(P = (\<not> P)) = False"
+  "((\<not> P) = (\<not> Q)) = (P = Q)"
+  "\<not> (P = (\<not> Q)) = (P = Q)"
+  "\<not> ((\<not> P) = Q) = (P = Q)"
+  "(P \<noteq> Q) = (Q = (\<not> P))"
+  "(P = Q) = ((\<not> P \<or> Q) \<and> (P \<or> \<not> Q))"
+  "(P \<noteq> Q) = ((\<not> P \<or> \<not> Q) \<and> (P \<or> Q))"
   by auto
 
 lemma [z3_new_rule]:
-  "(if P then P else \<not>P) = True"
-  "(if \<not>P then \<not>P else P) = True"
+  "(if P then P else \<not> P) = True"
+  "(if \<not> P then \<not> P else P) = True"
   "(if P then True else False) = P"
-  "(if P then False else True) = (\<not>P)"
-  "(if P then Q else True) = ((\<not>P) \<or> Q)"
-  "(if P then Q else True) = (Q \<or> (\<not>P))"
-  "(if P then Q else \<not>Q) = (P = Q)"
-  "(if P then Q else \<not>Q) = (Q = P)"
-  "(if P then \<not>Q else Q) = (P = (\<not>Q))"
-  "(if P then \<not>Q else Q) = ((\<not>Q) = P)"
-  "(if \<not>P then x else y) = (if P then y else x)"
-  "(if P then (if Q then x else y) else x) = (if P \<and> (\<not>Q) then y else x)"
-  "(if P then (if Q then x else y) else x) = (if (\<not>Q) \<and> P then y else x)"
+  "(if P then False else True) = (\<not> P)"
+  "(if P then Q else True) = ((\<not> P) \<or> Q)"
+  "(if P then Q else True) = (Q \<or> (\<not> P))"
+  "(if P then Q else \<not> Q) = (P = Q)"
+  "(if P then Q else \<not> Q) = (Q = P)"
+  "(if P then \<not> Q else Q) = (P = (\<not> Q))"
+  "(if P then \<not> Q else Q) = ((\<not> Q) = P)"
+  "(if \<not> P then x else y) = (if P then y else x)"
+  "(if P then (if Q then x else y) else x) = (if P \<and> (\<not> Q) then y else x)"
+  "(if P then (if Q then x else y) else x) = (if (\<not> Q) \<and> P then y else x)"
   "(if P then (if Q then x else y) else y) = (if P \<and> Q then x else y)"
   "(if P then (if Q then x else y) else y) = (if Q \<and> P then x else y)"
   "(if P then x else if P then y else z) = (if P then x else z)"
@@ -375,31 +375,31 @@
 
 lemma [z3_new_rule]:  (* for def-axiom *)
   "P = Q \<or> P \<or> Q"
-  "P = Q \<or> \<not>P \<or> \<not>Q"
-  "(\<not>P) = Q \<or> \<not>P \<or> Q"
-  "(\<not>P) = Q \<or> P \<or> \<not>Q"
-  "P = (\<not>Q) \<or> \<not>P \<or> Q"
-  "P = (\<not>Q) \<or> P \<or> \<not>Q"
-  "P \<noteq> Q \<or> P \<or> \<not>Q"
-  "P \<noteq> Q \<or> \<not>P \<or> Q"
-  "P \<noteq> (\<not>Q) \<or> P \<or> Q"
-  "(\<not>P) \<noteq> Q \<or> P \<or> Q"
-  "P \<or> Q \<or> P \<noteq> (\<not>Q)"
-  "P \<or> Q \<or> (\<not>P) \<noteq> Q"
-  "P \<or> \<not>Q \<or> P \<noteq> Q"
-  "\<not>P \<or> Q \<or> P \<noteq> Q"
+  "P = Q \<or> \<not> P \<or> \<not> Q"
+  "(\<not> P) = Q \<or> \<not> P \<or> Q"
+  "(\<not> P) = Q \<or> P \<or> \<not> Q"
+  "P = (\<not> Q) \<or> \<not> P \<or> Q"
+  "P = (\<not> Q) \<or> P \<or> \<not> Q"
+  "P \<noteq> Q \<or> P \<or> \<not> Q"
+  "P \<noteq> Q \<or> \<not> P \<or> Q"
+  "P \<noteq> (\<not> Q) \<or> P \<or> Q"
+  "(\<not> P) \<noteq> Q \<or> P \<or> Q"
+  "P \<or> Q \<or> P \<noteq> (\<not> Q)"
+  "P \<or> Q \<or> (\<not> P) \<noteq> Q"
+  "P \<or> \<not> Q \<or> P \<noteq> Q"
+  "\<not> P \<or> Q \<or> P \<noteq> Q"
   "P \<or> y = (if P then x else y)"
   "P \<or> (if P then x else y) = y"
-  "\<not>P \<or> x = (if P then x else y)"
-  "\<not>P \<or> (if P then x else y) = x"
-  "P \<or> R \<or> \<not>(if P then Q else R)"
-  "\<not>P \<or> Q \<or> \<not>(if P then Q else R)"
-  "\<not>(if P then Q else R) \<or> \<not>P \<or> Q"
-  "\<not>(if P then Q else R) \<or> P \<or> R"
-  "(if P then Q else R) \<or> \<not>P \<or> \<not>Q"
-  "(if P then Q else R) \<or> P \<or> \<not>R"
-  "(if P then \<not>Q else R) \<or> \<not>P \<or> Q"
-  "(if P then Q else \<not>R) \<or> P \<or> R"
+  "\<not> P \<or> x = (if P then x else y)"
+  "\<not> P \<or> (if P then x else y) = x"
+  "P \<or> R \<or> \<not> (if P then Q else R)"
+  "\<not> P \<or> Q \<or> \<not> (if P then Q else R)"
+  "\<not> (if P then Q else R) \<or> \<not> P \<or> Q"
+  "\<not> (if P then Q else R) \<or> P \<or> R"
+  "(if P then Q else R) \<or> \<not> P \<or> \<not> Q"
+  "(if P then Q else R) \<or> P \<or> \<not> R"
+  "(if P then \<not> Q else R) \<or> \<not> P \<or> Q"
+  "(if P then Q else \<not> R) \<or> P \<or> R"
   by auto
 
 hide_type (open) pattern




