problem([]==>x:int=>n:pnat=>l:int list=>member(x,nth(n,l))=>member(x,l),
ind_strat(induction(lemma(nat_list_pair)-[(l:int list)-v2::v1,(n:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1],[nth2,equ(int list,left)]),reduction([1],[member1,equ(u(1),left)]),reduction([2],[member1,equ(u(1),left)])]))then[elementary(intro(new[x])then[intro(new[v1])then[hyp(v1),wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([2,1],[nth1,equ(int list,left)])]))then[elementary(intro(new[x])then[intro(new[v1])then[hyp(v1),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,1],[nth3,equ(int list,left)],[])then[casesplit(disjunction([x=v2 in int=>void,x=v2 in int]))then[wave(direction_out,[2],[member3,equ(u(1),left)],[]),wave(direction_out,[2],[member2,complementary,equ(u(1),left)],[])]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v3)),idtac])]),lambda(v0,lambda(v1,lambda(v2,lambda(v3,su(su(su(v6,[v5 of v2],[v6]),[v4 of v0],[v5]),[v3 of v1],[v4]))of lambda(v0,lambda(v1,lambda(v2,lambda(v3,su(su(su(v6,[v5 of v1],[v6]),[v4 of v0],[v5]),[v3 of v2],[v4]))of lambda(l,lambda(n,su(lambda(v5,su(su(su(su(su(su(v11,[v10 of lambda(v0,lambda(v2,lambda(v1,lambda(v3,lambda(v4,su(su(su(su(lambda(v5,su(v6,[v5 of v4],[v6]))of lambda(x,lambda(v5,decide(v5,[v6,lambda(v4,su(su(su(su(su(su(v5,[v3 of x],[v5]),[v7 of v4],[v5]),[v6 of v1],[v7]),[v5 of v2],[v6]),[member3 of x],[v5]),[term_of(member3)],[member3]))of v6],[v7,lambda(v4,su(su(su(su(su(_79493,[v7 of v4],[v5]),[v6 of v1],[v7]),[v5 of v2],[v6]),[member2 of x],[v5]),[term_of(member2)],[member2]))of v7]))of su(su(su(v6,[v5 of v2],[v6]),[v4 of x],[v5]),[term_of(deceqint)],[v4])),[v6 of v1],[v7]),[v5 of v2],[v6]),[nth3 of v0],[v5]),[term_of(nth3)],[nth3]))))))],[v11]),[v9 of lambda(v0,lambda(v1,su(su(lambda(v2,su(v3,[v2 of v1],[v3]))of lambda(x,lambda(v1,v1)),[nth1 of v0],[v2]),[term_of(nth1)],[nth1])))],[v10]),[v8 of lambda(v0,lambda(v1,su(su(lambda(v2,su(v3,[v2 of v1],[v3]))of lambda(v1,su(su(lambda(v2,su(v3,[v2 of v1],[v3]))of lambda(v1,su(su(lambda(v2,su(v3,[v2 of v1],[v3]))of lambda(x,lambda(v1,v1)),[member1 of v1],[v2]),[term_of(member1)],[member1])),[member1 of v1],[v2]),[term_of(member1)],[member1])),[nth2 of v0],[v2]),[term_of(nth2)],[nth2])))],[v9]),[v7 of l],[v8]),[v6 of n],[v7]),[v5 of lambda(n,lambda(l,x:int=>member(x,nth(n,l))=>member(x,l)))],[v6]))of v4,[term_of(nat_list_pair)],[v4]))))))))),
[problem([l:int list,n:pnat,v0:pnat,v2:int,v1:int list,v3:x:int=>member(x,nth(v0,v1))=>member(x,v1),x:int,v4:x=v2 in int]==>member(x,nth(v0,v1))=>{true},
 elementary(intro(new[v5])then[istrue,wfftacs]),lambda(v5,0),
 [
 ]) ext _79493
]).
