src/FOL/FOL.thy
 changeset 14085 8dc3e532959a parent 13550 5a176b8dda84 child 14156 2072802ab0e3
```--- a/src/FOL/FOL.thy	Mon Jun 30 18:15:51 2003 +0200
+++ b/src/FOL/FOL.thy	Tue Jul 01 10:50:26 2003 +0200
@@ -43,6 +43,38 @@
setup Splitter.setup
setup Clasimp.setup

+subsection {* Other simple lemmas *}
+
+lemma [simp]: "((P-->R) <-> (Q-->R)) <-> ((P<->Q) | R)"
+by blast
+
+lemma [simp]: "((P-->Q) <-> (P-->R)) <-> (P --> (Q<->R))"
+by blast
+
+lemma not_disj_iff_imp: "~P | Q <-> (P-->Q)"
+by blast
+
+(** Monotonicity of implications **)
+
+lemma conj_mono: "[| P1-->Q1; P2-->Q2 |] ==> (P1&P2) --> (Q1&Q2)"
+by fast (*or (IntPr.fast_tac 1)*)
+
+lemma disj_mono: "[| P1-->Q1; P2-->Q2 |] ==> (P1|P2) --> (Q1|Q2)"
+by fast (*or (IntPr.fast_tac 1)*)
+
+lemma imp_mono: "[| Q1-->P1; P2-->Q2 |] ==> (P1-->P2)-->(Q1-->Q2)"
+by fast (*or (IntPr.fast_tac 1)*)
+
+lemma imp_refl: "P-->P"
+by (rule impI, assumption)
+
+(*The quantifier monotonicity rules are also intuitionistically valid*)
+lemma ex_mono: "(!!x. P(x) --> Q(x)) ==> (EX x. P(x)) --> (EX x. Q(x))"
+by blast
+
+lemma all_mono: "(!!x. P(x) --> Q(x)) ==> (ALL x. P(x)) --> (ALL x. Q(x))"
+by blast
+

subsection {* Proof by cases and induction *}
```