problem([]==>x:pnat=>plus(x,0)=x in pnat,
ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])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],v1)]))then elementary(identity)))])]),lambda(x,p_ind(x,su(su(axiom,[plus1 of 0],[v0]),[term_of(plus1)],[plus1]),[v0,v1,su(su(su(axiom,[v2 of 0],[v3]),[plus2 of v0],[v2]),[term_of(plus2)],[plus2])])),
[
]).
