problem([]==>i:pnat=>j:pnat=>l:int list=>nth(plus(i,j),l)=nth(j,nth(i,l))in int list,
ind_strat(induction(lemma(pnat_primitive)-[(i:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([2,2,1],[nth1,equ(int list,left)])]))then[elementary(intro(new[j])then[intro(new[l])then[identity,wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1,1],[plus2,equ(pnat,left)],[]))then[idtac])]),lambda(i,p_ind(i,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(j,lambda(l,axiom)),[nth1 of v1],[v2]),[term_of(nth1)],[nth1]))),[plus1 of v0],[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 _236544,[v4 of v2],[v5]),[plus2 of v0],[v4]),[term_of(plus2)],[plus2])))])),
[problem([i:pnat,v0:pnat,v1:j:pnat=>l:int list=>nth(plus(v0,j),l)=nth(j,nth(v0,l))in int list]==>j:pnat=>l:int list=>nth(s(plus(v0,j)),l)=nth(j,nth(s(v0),l))in int list,
 ind_strat(induction(lemma(list_primitive)-[(l:int list)-v3::v2])then[base_case(sym_eval(normalize_term([reduction([1,1],[nth2,equ(int list,left)]),reduction([2,2,1],[nth2,equ(int list,left)]),reduction([2,1],[nth2,equ(int list,left)])]))then[elementary(intro(new[j])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[nth3,equ(int list,left)],[])then[wave(direction_out,[2,2,1],[nth3,equ(int list,left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])]),lambda(v2,lambda(v3,lambda(v4,su(su(v6,[v5 of v2],[v6]),[v4 of v3],[v5]))of lambda(l,list_ind(l,lambda(v2,su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(j,axiom),[nth2 of v2],[v3]),[term_of(nth2)],[nth2])),[nth2 of s(v0)],[v3]),[term_of(nth2)],[nth2])),[nth2 of s(plus(v0,v2))],[v3]),[term_of(nth2)],[nth2])),[v3,v2,v4,lambda(v5,su(su(su(su(lambda(v6,su(v7,[v6 of v5],[v7]))of lambda(v5,su(su(su(su(lambda(v6,su(v7,[v6 of v5],[v7]))of lambda(j,su(su(v6,[v5 of v2],[v6]),[v1 of j],[v5])),[v7 of v2],[v8]),[v6 of v3],[v7]),[nth3 of v0],[v6]),[term_of(nth3)],[nth3])),[v7 of v2],[v8]),[v6 of v3],[v7]),[nth3 of plus(v0,v5)],[v6]),[term_of(nth3)],[nth3]))])))),
 [
 ]) ext _236544
]).
