(* Title: FOLP/ex/if ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1991 University of Cambridge For ex/if.thy. First-Order Logic: the 'if' example *) open If; open Cla; (*in case structure Int is open!*) val prems = goalw If.thy [if_def] "[| !!x. x:P ==> f(x):Q; !!x. x:~P ==> g(x):R |] ==> ?p:if(P,Q,R)"; by (fast_tac (FOLP_cs addIs prems) 1); val ifI = result(); val major::prems = goalw If.thy [if_def] "[| p:if(P,Q,R); !!x y.[| x:P; y:Q |] ==> f(x,y):S; \ \ !!x y.[| x:~P; y:R |] ==> g(x,y):S |] ==> ?p:S"; by (cut_facts_tac [major] 1); by (fast_tac (FOLP_cs addIs prems) 1); val ifE = result(); Goal "?p : if(P, if(Q,A,B), if(Q,C,D)) <-> if(Q, if(P,A,C), if(P,B,D))"; by (rtac iffI 1); by (etac ifE 1); by (etac ifE 1); by (rtac ifI 1); by (rtac ifI 1); choplev 0; val if_cs = FOLP_cs addSIs [ifI] addSEs[ifE]; by (fast_tac if_cs 1); val if_commute = result(); Goal "?p : if(if(P,Q,R), A, B) <-> if(P, if(Q,A,B), if(R,A,B))"; by (fast_tac if_cs 1); val nested_ifs = result(); writeln"Reached end of file.";