problem([]==>e:int=>l1:int list=>l2:int list=>(member(e,l1)\member(e,l2))=>member(e,app(l1,l2)),
ind_strat(induction(lemma(list_primitive)-[(l1:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1,1],[member1,equ(u(1),left)]),reduction([2,2],[app1,equ(int list,left)])]))then[elementary(intro(new[e])then[intro(new[l2])then[intro(new[v0])then[elim(v0)then[elim(v1),hyp(v2)],wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,2],[app2,equ(int list,left)],[])then[casesplit(disjunction([e=v1 in int=>void,e=v1 in int]))then[wave(direction_out,[2],[member3,equ(u(1),left)],[])then[wave(direction_out,[1,1],[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,v2)),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(l1,list_ind(l1,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(e,lambda(l2,lambda(v0,decide(v0,[v1,any(v1)],[v2,v2])))),[app1 of v1],[v2]),[term_of(app1)],[app1]))),[member1 of v0],[v2]),[term_of(member1)],[member1]))),[v1,v0,v2,lambda(v3,lambda(v4,su(su(su(su(lambda(v5,su(su(v7,[v6 of v4],[v7]),[v5 of v3],[v6]))of lambda(e,lambda(v4,decide(v4,[v5,lambda(v3,lambda(v4,su(su(su(su(su(lambda(v5,su(v6,[v5 of v4],[v6]))of lambda(v4,su(su(su(su(su(lambda(v5,su(v6,[v5 of v4],[v6]))of lambda(l2,su(su(v5,[v4 of l2],[v5]),[v2 of e],[v4])),[v7 of v3],[v5]),[v6 of v0],[v7]),[v5 of v1],[v6]),[member3 of e],[v5]),[term_of(member3)],[member3])),[v7 of v3],[v5]),[v6 of app(v0,v4)],[v7]),[v5 of v1],[v6]),[member3 of e],[v5]),[term_of(member3)],[member3])))of v5],[v6,lambda(v3,lambda(v4,su(su(su(su(su(lambda(v5,su(v6,[v5 of v4],[v6]))of _147130,[v7 of v3],[v5]),[v6 of app(v0,v4)],[v7]),[v5 of v1],[v6]),[member2 of e],[v5]),[term_of(member2)],[member2])))of v6]))of su(su(su(v5,[v4 of v1],[v5]),[v3 of e],[v4]),[term_of(deceqint)],[v3])),[v6 of v4],[v7]),[v5 of v0],[v6]),[app2 of v1],[v5]),[term_of(app2)],[app2])))]))))),
[problem([l1:int list,v1:int,v0:int list,v2:e:int=>l2:int list=>(member(e,v0)\member(e,l2))=>member(e,app(v0,l2)),e:int,v3:e=v1 in int]==>l2:int list=>(member(e,v1::v0)\member(e,l2))=>{true},
 elementary(intro(new[l2])then[intro(new[v4])then[istrue,wfftacs],wfftacs]),lambda(l2,lambda(v4,0)),
 [
 ]) ext _147130
]).
