/*
 * @(#)$Id: binom,v 1.1 1994/09/16 09:34:53 dream Exp $
 *
 * $Log: binom,v $
 * Revision 1.1  1994/09/16 09:34:53  dream
 * Initial revision
 *
 */

problem([]==>pnat=>pnat=>pnat,
intro then wfftacs,lambda(v0,_8760),
[problem([v0:pnat]==>pnat=>pnat,
 elim(v0),p_ind(v0,_8786,[v1,v2,_8792]),
 [problem([v0:pnat]==>pnat=>pnat,
  intro then wfftacs,lambda(v1,_8820),
  [problem([v0:pnat,v1:pnat]==>pnat,
   decide(v1=0 in pnat)then wfftacs,pnat_eq(v1,0,su(_8861,[axiom],[v2]),su(_8869,[lambda(~,axiom)],[v2])),
   [problem([v0:pnat,v1:pnat,v2:v1=0 in pnat]==>pnat,
    intro(explicit(s(0)))then wfftacs,s(0),
    [
    ]) ext _8861,
    problem([v0:pnat,v1:pnat,v2:v1=0 in pnat=>void]==>pnat,
    intro(0),0,
    [
    ]) ext _8869
   ]) ext _8820
  ]) ext _8786,
  problem([v0:pnat,v1:pnat,v2:pnat=>pnat]==>pnat=>pnat,
  pure(intro)then wfftacs,lambda(v3,_9004),
  [problem([v0:pnat,v1:pnat,v2:pnat=>pnat,v3:pnat]==>pnat,
   elim(v3),p_ind(v3,_9045,[v4,v5,_9051]),
   [problem([v0:pnat,v1:pnat,v2:pnat=>pnat,v3:pnat]==>pnat,
    intro(explicit(s(0)))then wfftacs,s(0),
    [
    ]) ext _9045,
    problem([v0:pnat,v1:pnat,v2:pnat=>pnat,v3:pnat,v4:pnat,v5:pnat]==>pnat,
    intro(explicit(plus(v2 of s(v4),v2 of v4)))then wfftacs,plus(v2 of s(v4),v2 of v4),
    [
    ]) ext _9051
   ]) ext _9004
  ]) ext _8792
 ]) ext _8760
]).
