/*
 * @(#)$Id: identrm,v 1.1 1994/09/16 09:39:18 dream Exp $
 *
 * $Log: identrm,v $
 * Revision 1.1  1994/09/16 09:39:18  dream
 * Initial revision
 *
 */

problem([]==>x:pnat=>times(x,s(0))=x in pnat,
autotactic(idtac),_125,
[problem([]==>x:pnat=>times(x,s(0))=x in pnat,
 dequantify,lambda(x,_181),
 [problem([x:pnat]==>times(x,s(0))=x in pnat,
  induction(s(v0),x:pnat),p_ind(x,_221,[v0,v1,_227]),
  [problem([x:pnat]==>times(0,s(0))=0 in pnat,
   base([1,1],times1),su(_266,[term_of(times1)],[times1]),
   [problem([x:pnat]==>0=0 in pnat,
    identity,axiom,
    [
    ]) ext _266
   ]) ext _221,
   problem([x:pnat,v0:pnat,v1:times(v0,s(0))=v0 in pnat]==>times(s(v0),s(0))=s(v0)in pnat,
   wave([1,1],times2),su(_364,[term_of(times2)],[times2]),
   [problem([x:pnat,v0:pnat,v1:times(v0,s(0))=v0 in pnat]==>plus(times(v0,s(0)),s(0))=s(v0)in pnat,
    fertilize_left([1],v1),_381,
    [problem([x:pnat,v0:pnat,v1:times(v0,s(0))=v0 in pnat]==>plus(v0,s(0))=s(v0)in pnat,
     induction(s(v0),v0:pnat),p_ind(v0,_497,[v2,v3,_503]),
     [problem([x:pnat,v0:pnat,v1:times(v0,s(0))=v0 in pnat]==>plus(0,s(0))=s(0)in pnat,
      base([1,1],plus1),su(_565,[term_of(plus1)],[plus1]),
      [problem([x:pnat,v0:pnat,v1:times(v0,s(0))=v0 in pnat]==>s(0)=s(0)in pnat,
       identity,axiom,
       [
       ]) ext _565
      ]) ext _497,
      problem([x:pnat,v0:pnat,v1:times(v0,s(0))=v0 in pnat,v2:pnat,v3:plus(v2,s(0))=s(v2)in pnat]==>plus(s(v2),s(0))=s(s(v2))in pnat,
      wave([1,1],plus2),su(_713,[term_of(plus2)],[plus2]),
      [problem([x:pnat,v0:pnat,v1:times(v0,s(0))=v0 in pnat,v2:pnat,v3:plus(v2,s(0))=s(v2)in pnat]==>s(plus(v2,s(0)))=s(s(v2))in pnat,
       fertilize_right([1],v3),_730,
       [problem([x:pnat,v0:pnat,v1:times(v0,s(0))=v0 in pnat,v2:pnat,v3:plus(v2,s(0))=s(v2)in pnat]==>s(plus(v2,s(0)))=s(plus(v2,s(0)))in pnat,
        identity,axiom,
        [
        ]) ext _730
       ]) ext _713
      ]) ext _503
     ]) ext _381
    ]) ext _364
   ]) ext _227
  ]) ext _181
 ]) ext _125
]).
