problem([]==>x:pnat=>y:pnat=>z:pnat=>plus(x,plus(y,z))=plus(plus(x,y),z)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)]),reduction([1,2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[y])then[intro(new[z])then[identity,wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[],[cnc_s,imp(right)],[])]]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])]),lambda(x,p_ind(x,lambda(v0,lambda(v1,su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of lambda(v0,lambda(v1,su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of lambda(y,lambda(z,axiom)),[plus1 of v0],[v2]),[term_of(plus1)],[plus1]))),[plus1 of plus(v0,v1)],[v2]),[term_of(plus1)],[plus1]))),[v0,v1,lambda(v2,lambda(v3,su(su(su(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of lambda(v2,lambda(v3,su(su(su(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of lambda(v2,lambda(v3,su(su(su(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of lambda(v2,lambda(v3,su(su(su(su(v4,[v5 of(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of v1)],[v4]),[v4 of plus(plus(v0,v2),v3)],[v5]),[cnc_s of plus(v0,plus(v2,v3))],[v4]),[term_of(cnc_s)],[cnc_s]))),[v4 of v3],[v5]),[plus2 of plus(v0,v2)],[v4]),[term_of(plus2)],[plus2]))),[v4 of v2],[v5]),[plus2 of v0],[v4]),[term_of(plus2)],[plus2]))),[v4 of plus(v2,v3)],[v5]),[plus2 of v0],[v4]),[term_of(plus2)],[plus2])))])),
[
]).
