doc-src/ZF/IFOL_examples.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-src/ZF/IFOL_examples.thy	Tue Aug 19 13:53:58 2003 +0200
@@ -0,0 +1,58 @@
+header{*Examples of Intuitionistic Reasoning*}
+
+theory IFOL_examples = IFOL:
+
+text{*Quantifier example from the book Logic and Computation*}
+lemma "(EX y. ALL x. Q(x,y)) -->  (ALL x. EX y. Q(x,y))"
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (rule impI)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (rule allI)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (rule exI)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (erule exE)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (erule allE)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+txt{*Now @{text "apply assumption"} fails*}
+oops
+
+text{*Trying again, with the same first two steps*}
+lemma "(EX y. ALL x. Q(x,y)) -->  (ALL x. EX y. Q(x,y))"
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (rule impI)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (rule allI)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (erule exE)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (rule exI)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (erule allE)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply assumption
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+done
+
+lemma "(EX y. ALL x. Q(x,y)) -->  (ALL x. EX y. Q(x,y))"
+by (tactic {*IntPr.fast_tac 1*})
+
+text{*Example of Dyckhoff's method*}
+lemma "~ ~ ((P-->Q) | (Q-->P))"
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (unfold not_def)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (rule impI)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (erule disj_impE)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply (erule imp_impE)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+ apply (erule imp_impE)
+  --{* @{subgoals[display,indent=0,margin=65]} *}
+apply assumption 
+apply (erule FalseE)+
+done
+
+end