# File If.ML

    (*  Title:      FOLP/ex/If.ML
        ID:         $Id: If.ML,v 1.5 2005/09/18 12:25:49 wenzelm Exp $
        Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
        Copyright   1991  University of Cambridge
    *)

    val prems = goalw (the_context ()) [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 (the_context ()) [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();