problem([]==>x:pnat=>y:pnat=>z:pnat=>times(times(z,x),y)=times(times(z,y),x)in pnat,
ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[idtac,step_case(ripple(direction_out,wave(direction_out,[2,1],[times2right,equ(pnat,left)],[])then[wave(direction_out,[1,1,1],[times2right,equ(pnat,left)],[])then[wave(direction_out,[1,1],[disttwo,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,[2],v1)]))then elementary(intro(new[y])then[intro(new[z])then[identity,wfftacs],wfftacs])))])]),lambda(x,p_ind(x,_170129,[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(su(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of lambda(v2,lambda(v3,su(su(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of lambda(y,lambda(z,axiom)),[v4 of v3],[v5]),[v1 of v2],[v4]))),[v5 of times(v3,v0)],[v6]),[v4 of v3],[v5]),[disttwo of v2],[v4]),[term_of(disttwo)],[disttwo]))),[v4 of v0],[v5]),[times2right of v3],[v4]),[term_of(times2right)],[times2right]))),[v4 of v0],[v5]),[times2right of times(v3,v2)],[v4]),[term_of(times2right)],[times2right])))])),
[problem([x:pnat]==>y:pnat=>z:pnat=>times(times(z,0),y)=times(times(z,y),0)in pnat,
 ind_strat(induction(lemma(pnat_primitive)-[(y:pnat)-s(v0)])then[base_case(elementary(intro(new[z])then[identity,wfftacs])),step_case(ripple(direction_out,wave(direction_out,[1,1],[times2right,equ(pnat,left)],[])then[wave(direction_out,[1,2,1],[times2right,equ(pnat,left)],[])then[wave(direction_out,[2,1],[disttwo,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,[2],v1)]))then elementary(intro(new[z])then[identity,wfftacs])))])]),lambda(y,p_ind(y,lambda(z,axiom),[v0,v1,lambda(v2,su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(z,axiom),[v1 of v2],[v3])),[v4 of times(v2,v0)],[v5]),[v3 of v2],[v4]),[disttwo of 0],[v3]),[term_of(disttwo)],[disttwo])),[v3 of v0],[v4]),[times2right of v2],[v3]),[term_of(times2right)],[times2right])),[v3 of v0],[v4]),[times2right of times(v2,0)],[v3]),[term_of(times2right)],[times2right]))])),
 [
 ]) ext _170129
]).
