problem([]==>a:pnat=>b:pnat=>plus(a,b)=plus(b,a)in pnat,
ind_strat(induction(lemma(pnat_primitive)-[(a:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)])]))),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(left,[weak_fertilize(left,in,[1],v1)]))))])]),lambda(a,p_ind(a,lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of _137214,[plus1 of v0],[v1]),[term_of(plus1)],[plus1])),[v0,v1,lambda(v2,su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(lambda(v3,su(v4,[v3 of v2],[v4]))of _137139,[v1 of v2],[v3])),[v3 of v2],[v4]),[plus2 of v0],[v3]),[term_of(plus2)],[plus2]))])),
[problem([a:pnat]==>b:pnat=>b=plus(b,0)in pnat,
 ind_strat(induction(lemma(pnat_primitive)-[(b:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[2,1],[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(b,p_ind(b,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])])),
 [
 ]) ext _137214,
 problem([a:pnat,v0:pnat,v1:b:pnat=>plus(v0,b)=plus(b,v0)in pnat]==>b:pnat=>s(plus(b,v0))=plus(b,s(v0))in pnat,
 ind_strat(induction(lemma(pnat_primitive)-[(b:pnat)-s(v2)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1,1],[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],v3)]))then elementary(identity)))])]),lambda(b,p_ind(b,su(su(su(su(axiom,[plus1 of s(v0)],[v2]),[term_of(plus1)],[plus1]),[plus1 of v0],[v2]),[term_of(plus1)],[plus1]),[v2,v3,su(su(su(su(su(su(axiom,[v4 of v0],[v5]),[plus2 of v2],[v4]),[term_of(plus2)],[plus2]),[v4 of s(v0)],[v5]),[plus2 of v2],[v4]),[term_of(plus2)],[plus2])])),
 [
 ]) ext _137139
]).
