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

problem([]==>x:{posint}=>y:{posint}=>divides(x,y)\divides(x,y)=>void,
repeat intro then try wfftacs,lambda(x,lambda(y,_242)),
[problem([x:{posint},y:{posint}]==>divides(x,y)\divides(x,y)=>void,
 seq(z:{posint}=>z<*s(y)=>(w:{posint}#w<*s(z)#y=times(w,x))\w:{posint}=>w<*s(z)#y=times(w,x)in{posint}=>void,new[v0]),lambda(v0,_365)of _362,
 [problem([x:{posint},y:{posint}]==>z:{posint}=>z<*s(y)=>(w:{posint}#w<*s(z)#y=times(w,x))\w:{posint}=>w<*s(z)#y=times(w,x)in{posint}=>void,
  repeat intro then try wfftacs,lambda(z,lambda(v0,_476)),
  [problem([x:{posint},y:{posint},z:{posint},v0:z<*s(y)]==>(w:{posint}#w<*s(z)#y=times(w,x))\w:{posint}=>w<*s(z)#y=times(w,x)in{posint}=>void,
   compute(hyp(z),[[simplify]]),_485,
   [problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y)]==>(w:{posint}#w<*s(z)#y=times(w,x))\w:{posint}=>w<*s(z)#y=times(w,x)in{posint}=>void,
    elim(z)then try wfftacs,su(_701,[z,assert(greater(z,0))],[v1,v2]),
    [problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat]==>(w:{posint}#w<*s(v1)#y=times(w,x))\w:{posint}=>w<*s(v1)#y=times(w,x)in{posint}=>void,
     elim(v1),p_ind(v1,_853,[v4,v5,_859]),
     [problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat]==>(w:{posint}#w<*s(0)#y=times(w,x))\w:{posint}=>w<*s(0)#y=times(w,x)in{posint}=>void,
      intro(right)then apply(because),inr(atom(incomplete)),
      [
      ]) ext _853,
      problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat,v4:pnat,v5:(w:{posint}#w<*s(v4)#y=times(w,x))\w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void]==>(w:{posint}#w<*s(s(v4))#y=times(w,x))\w:{posint}=>w<*s(s(v4))#y=times(w,x)in{posint}=>void,
      elim(v5)then thin([v8,v9]),decide(v5,[v6,_1222],[v7,_1226]),
      [problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat,v4:pnat,v5:(w:{posint}#w<*s(v4)#y=times(w,x))\w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v6:w:{posint}#w<*s(v4)#y=times(w,x)]==>(w:{posint}#w<*s(s(v4))#y=times(w,x))\w:{posint}=>w<*s(s(v4))#y=times(w,x)in{posint}=>void,
       intro(left)then try wfftacs,inl(_1464),
       [problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat,v4:pnat,v5:(w:{posint}#w<*s(v4)#y=times(w,x))\w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v6:w:{posint}#w<*s(v4)#y=times(w,x)]==>w:{posint}#w<*s(s(v4))#y=times(w,x),
        intro(explicit(v6))then wfftacs,v6,
        [
        ]) ext _1464
       ]) ext _1222,
       problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat,v4:pnat,v5:(w:{posint}#w<*s(v4)#y=times(w,x))\w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v7:w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void]==>(w:{posint}#w<*s(s(v4))#y=times(w,x))\w:{posint}=>w<*s(s(v4))#y=times(w,x)in{posint}=>void,
       decide(y=times(s(v4),x)in pnat),pnat_eq(y,times(s(v4),x),su(_1925,[axiom],[v6]),su(_1933,[lambda(~,axiom)],[v6])),
       [problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat,v4:pnat,v5:(w:{posint}#w<*s(v4)#y=times(w,x))\w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v7:w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v6:y=times(s(v4),x)in pnat]==>(w:{posint}#w<*s(s(v4))#y=times(w,x))\w:{posint}=>w<*s(s(v4))#y=times(w,x)in{posint}=>void,
        intro(left)then try wfftacs,inl(_2203),
        [problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat,v4:pnat,v5:(w:{posint}#w<*s(v4)#y=times(w,x))\w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v7:w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v6:y=times(s(v4),x)in pnat]==>w:{posint}#w<*s(s(v4))#y=times(w,x),
         intro(s(v4))then try wfftacs,s(v4)&_2432,
         [problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat,v4:pnat,v5:(w:{posint}#w<*s(v4)#y=times(w,x))\w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v7:w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v6:y=times(s(v4),x)in pnat]==>s(v4)<*s(s(v4))#y=times(s(v4),x),
          because,atom(incomplete),
          [
          ]) ext _2432
         ]) ext _2203
        ]) ext _1925,
        problem([x:{posint},y:{posint},z:{p:pnat\greater(p,0)},v0:z<*s(y),v1:pnat,v2:greater(z,0),v3:v1=z in pnat,v4:pnat,v5:(w:{posint}#w<*s(v4)#y=times(w,x))\w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v7:w:{posint}=>w<*s(v4)#y=times(w,x)in{posint}=>void,v6:y=times(s(v4),x)in pnat=>void]==>(w:{posint}#w<*s(s(v4))#y=times(w,x))\w:{posint}=>w<*s(s(v4))#y=times(w,x)in{posint}=>void,
        intro(right)then apply(because),inr(atom(incomplete)),
        [
        ]) ext _1933
       ]) ext _1226
      ]) ext _859
     ]) ext _701
    ]) ext _485
   ]) ext _476
  ]) ext _362,
  problem([x:{posint},y:{posint},v0:z:{posint}=>z<*s(y)=>(w:{posint}#w<*s(z)#y=times(w,x))\w:{posint}=>w<*s(z)#y=times(w,x)in{posint}=>void]==>divides(x,y)\divides(x,y)=>void,
  do_elim_on(v0,[y],[v0,v1])then (append([],[v1],[v1])',' thin([])),su(_3058,[v0 of y],[v1]),
  [problem([x:{posint},y:{posint},v0:z:{posint}=>z<*s(y)=>(w:{posint}#w<*s(z)#y=times(w,x))\w:{posint}=>w<*s(z)#y=times(w,x)in{posint}=>void,v1:y<*s(y)=>(w:{posint}#w<*s(y)#y=times(w,x))\w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void]==>divides(x,y)\divides(x,y)=>void,
   elim(v1)then try wfftacs,su(_3259,[v1 of _3266],[v2]),
   [problem([x:{posint},y:{posint},v0:z:{posint}=>z<*s(y)=>(w:{posint}#w<*s(z)#y=times(w,x))\w:{posint}=>w<*s(z)#y=times(w,x)in{posint}=>void,v1:y<*s(y)=>(w:{posint}#w<*s(y)#y=times(w,x))\w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void]==>y<*s(y),
    arith then try wfftacs,axiom,
    [
    ]) ext _3266,
    problem([x:{posint},y:{posint},v0:z:{posint}=>z<*s(y)=>(w:{posint}#w<*s(z)#y=times(w,x))\w:{posint}=>w<*s(z)#y=times(w,x)in{posint}=>void,v1:y<*s(y)=>(w:{posint}#w<*s(y)#y=times(w,x))\w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void,v2:(w:{posint}#w<*s(y)#y=times(w,x))\w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void]==>divides(x,y)\divides(x,y)=>void,
    thin([v0,v1])then thinelim(v2),decide(v2,[v0,_3710],[v1,_3714]),
    [problem([x:{posint},y:{posint},v2:(w:{posint}#w<*s(y)#y=times(w,x))\w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void,v0:w:{posint}#w<*s(y)#y=times(w,x)]==>divides(x,y)\divides(x,y)=>void,
     intro(left)then try wfftacs,inl(_3850),
     [problem([x:{posint},y:{posint},v2:(w:{posint}#w<*s(y)#y=times(w,x))\w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void,v0:w:{posint}#w<*s(y)#y=times(w,x)]==>divides(x,y),
      compute([[unfold]]),_3859,
      [problem([x:{posint},y:{posint},v2:(w:{posint}#w<*s(y)#y=times(w,x))\w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void,v0:w:{posint}#w<*s(y)#y=times(w,x)]==>z:{posint}#y=times(x,z)in{posint},
       elim(v0),spread(v0,[w,v1,_4116]),
       [problem([x:{posint},y:{posint},v2:(w:{posint}#w<*s(y)#y=times(w,x))\w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void,v0:w:{posint}#w<*s(y)#y=times(w,x),w:{posint},v1:w<*s(y)#y=times(w,x),v3:v0=w&v1 in (w:{posint}#w<*s(y)#y=times(w,x))]==>z:{posint}#y=times(x,z)in{posint},
        intro(w)then apply(because),w&atom(incomplete),
        [
        ]) ext _4116
       ]) ext _3859
      ]) ext _3850
     ]) ext _3710,
     problem([x:{posint},y:{posint},v2:(w:{posint}#w<*s(y)#y=times(w,x))\w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void,v1:w:{posint}=>w<*s(y)#y=times(w,x)in{posint}=>void]==>divides(x,y)\divides(x,y)=>void,
     intro(right)then apply(because),inr(atom(incomplete)),
     [
     ]) ext _3714
    ]) ext _3259
   ]) ext _3058
  ]) ext _365
 ]) ext _242
]).
