problem([]==>x:pnat=>times(x,0)=0 in pnat,
ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[times1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,1],[times2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[],v1)]))))])]),lambda(x,p_ind(x,su(su(axiom,[times1 of 0],[v0]),[term_of(times1)],[times1]),[v0,v1,su(su(su(_118686,[v2 of 0],[v3]),[times2 of v0],[v2]),[term_of(times2)],[times2])])),
[problem([x:pnat,v0:pnat,v1:times(v0,0)=0 in pnat]==>plus(times(v0,0),0)=times(v0,0)in pnat,
 generalise(times(v0,0),v2:pnat),lambda(v2,su(v3,[v2 of times(v0,0)],[v3]))of _118603,
 [problem([x:pnat,v0:pnat,v1:times(v0,0)=0 in pnat]==>v2:pnat=>plus(v2,0)=v2 in pnat,
  ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,1],[plus2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[1],v4)]))then elementary(identity)))])]),lambda(v2,p_ind(v2,su(su(axiom,[plus1 of 0],[v3]),[term_of(plus1)],[plus1]),[v3,v4,su(su(su(axiom,[v5 of 0],[v6]),[plus2 of v3],[v5]),[term_of(plus2)],[plus2])])),
  [
  ]) ext _118603
 ]) ext _118686
]).
