src/FOLP/ex/intro.ML

made major changes to grammar;
added call of Type.infer_types to automatically eliminate ambiguities

(*  Title: 	FOL/ex/intro
    ID:         $Id$
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1992  University of Cambridge

Examples for the manual "Introduction to Isabelle"

Derives some inference rules, illustrating the use of definitions

To generate similar output to manual, execute these commands:
    Pretty.setmargin 72; print_depth 0;
*)


(**** Some simple backward proofs ****)

goal FOLP.thy "?p:P|P --> P";
by (resolve_tac [impI] 1);
by (resolve_tac [disjE] 1);
by (assume_tac 3);
by (assume_tac 2);
by (assume_tac 1);
val mythm = result();

goal FOLP.thy "?p:(P & Q) | R  --> (P | R)";
by (resolve_tac [impI] 1);
by (eresolve_tac [disjE] 1);
by (dresolve_tac [conjunct1] 1);
by (resolve_tac [disjI1] 1);
by (resolve_tac [disjI2] 2);
by (REPEAT (assume_tac 1));
result();

(*Correct version, delaying use of "spec" until last*)
goal FOLP.thy "?p:(ALL x y.P(x,y))  -->  (ALL z w.P(w,z))";
by (resolve_tac [impI] 1);
by (resolve_tac [allI] 1);
by (resolve_tac [allI] 1);
by (dresolve_tac [spec] 1);
by (dresolve_tac [spec] 1);
by (assume_tac 1);
result();


(**** Demonstration of fast_tac ****)

goal FOLP.thy "?p:(EX y. ALL x. J(y,x) <-> ~J(x,x))  \
\       -->  ~ (ALL x. EX y. ALL z. J(z,y) <-> ~ J(z,x))";
by (fast_tac FOLP_cs 1);
result();

goal FOLP.thy "?p:ALL x. P(x,f(x)) <-> \
\       (EX y. (ALL z. P(z,y) --> P(z,f(x))) & P(x,y))";
by (fast_tac FOLP_cs 1);
result();


(**** Derivation of conjunction elimination rule ****)

val [major,minor] = goal FOLP.thy "[| p:P&Q; !!x y.[| x:P; y:Q |] ==>f(x,y):R |] ==> ?p:R";
by (resolve_tac [minor] 1);
by (resolve_tac [major RS conjunct1] 1);
by (resolve_tac [major RS conjunct2] 1);
prth (topthm());
result();


(**** Derived rules involving definitions ****)

(** Derivation of negation introduction **)

val prems = goal FOLP.thy "(!!x.x:P ==> f(x):False) ==> ?p:~P";
by (rewrite_goals_tac [not_def]);
by (resolve_tac [impI] 1);
by (resolve_tac prems 1);
by (assume_tac 1);
result();

val [major,minor] = goal FOLP.thy "[| p:~P;  q:P |] ==> ?p:R";
by (resolve_tac [FalseE] 1);
by (resolve_tac [mp] 1);
by (resolve_tac [rewrite_rule [not_def] major] 1);
by (resolve_tac [minor] 1);
result();

(*Alternative proof of above result*)
val [major,minor] = goalw FOLP.thy [not_def]
    "[| p:~P;  q:P |] ==> ?p:R";
by (resolve_tac [minor RS (major RS mp RS FalseE)] 1);
result();

writeln"Reached end of file.";