problem([]==>x:pnat=>x<*s(x),
intro,lambda(x,_1189),
[problem([x:pnat]==>x<*s(x),
 elim(x),p_ind(x,_1217,[v0,v1,_1223]),
 [problem([x:pnat]==>0<*s(0),
  intro,axiom,
  [
  ]) ext _1217,
  problem([x:pnat,v0:pnat,v1:v0<*s(v0)]==>s(v0)<*s(s(v0)),
  arith(<*),axiom,
  [problem([x:pnat,v0:pnat,v1:v0<*s(v0)]==>v0<*s(v0),
   intro,v1,
   [
   ])
  ]) ext _1223
 ]) ext _1189,
 problem([]==>pnat in u(1),
 intro,axiom,
 [
 ])
]).
