src/FOL/ex/Intro.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Intro.thy	Wed Jun 07 23:21:55 2006 +0200
@@ -0,0 +1,102 @@
+(*  Title:      FOL/ex/Intro.thy
+    ID:         $Id$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1992  University of Cambridge
+
+Derives some inference rules, illustrating the use of definitions.
+*)
+
+header {* Examples for the manual ``Introduction to Isabelle'' *}
+
+theory Intro
+imports FOL
+begin
+
+subsubsection {* Some simple backward proofs *}
+
+lemma mythm: "P|P --> P"
+apply (rule impI)
+apply (rule disjE)
+prefer 3 apply (assumption)
+prefer 2 apply (assumption)
+apply assumption
+done
+
+lemma "(P & Q) | R --> (P | R)"
+apply (rule impI)
+apply (erule disjE)
+apply (drule conjunct1)
+apply (rule disjI1)
+apply (rule_tac [2] disjI2)
+apply assumption+
+done
+
+(*Correct version, delaying use of "spec" until last*)
+lemma "(ALL x y. P(x,y)) --> (ALL z w. P(w,z))"
+apply (rule impI)
+apply (rule allI)
+apply (rule allI)
+apply (drule spec)
+apply (drule spec)
+apply assumption
+done
+
+
+subsubsection {* Demonstration of @{text "fast"} *}
+
+lemma "(EX y. ALL x. J(y,x) <-> ~J(x,x))
+        -->  ~ (ALL x. EX y. ALL z. J(z,y) <-> ~ J(z,x))"
+apply fast
+done
+
+
+lemma "ALL x. P(x,f(x)) <->
+        (EX y. (ALL z. P(z,y) --> P(z,f(x))) & P(x,y))"
+apply fast
+done
+
+
+subsubsection {* Derivation of conjunction elimination rule *}
+
+lemma
+  assumes major: "P&Q"
+    and minor: "[| P; Q |] ==> R"
+  shows R
+apply (rule minor)
+apply (rule major [THEN conjunct1])
+apply (rule major [THEN conjunct2])
+done
+
+
+subsection {* Derived rules involving definitions *}
+
+text {* Derivation of negation introduction *}
+
+lemma
+  assumes "P ==> False"
+  shows "~ P"
+apply (unfold not_def)
+apply (rule impI)
+apply (rule prems)
+apply assumption
+done
+
+lemma
+  assumes major: "~P"
+    and minor: P
+  shows R
+apply (rule FalseE)
+apply (rule mp)
+apply (rule major [unfolded not_def])
+apply (rule minor)
+done
+
+text {* Alternative proof of the result above *}
+lemma
+  assumes major: "~P"
+    and minor: P
+  shows R
+apply (rule minor [THEN major [unfolded not_def, THEN mp, THEN FalseE]])
+done
+
+end