problem([]==>x:int=>y:int list=>member(x,y)=>member(x,rev(y)),
ind_strat(induction(lemma(list_primitive)-[(y:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1],[member1,equ(u(1),left)]),reduction([2,2],[rev1,equ(int list,left)]),reduction([2],[member1,equ(u(1),left)])]))then[elementary(intro(new[x])then[intro(new[v0])then[hyp(v0),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,2],[rev2,equ(int list,left)],[])then[wave(direction_out,[2],[memapp3,imp(right)],[])then[casesplit(disjunction([x=v1 in int=>void,x=v1 in int]))then[wave(direction_out,[1],[member3,equ(u(1),left)],[]),wave(direction_out,[1],[member2,complementary,equ(u(1),left)],[])]]])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,=>,[1],v2)])then ripple_and_cancel([unblock(wave_front,[2,2],[member3,equ(u(1),left)]),unblock(wave_front,[2,2],[member1,equ(u(1),left)])]))then elementary(intro(new[v4])then[intro(left)then[hyp(v4),wfftacs],wfftacs]))),idtac])]),lambda(v0,lambda(v1,lambda(v2,su(su(v4,[v3 of v0],[v4]),[v2 of v1],[v3]))of lambda(y,list_ind(y,lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(x,lambda(v0,v0)),[member1 of v0],[v1]),[term_of(member1)],[member1])),[term_of(rev1)],[rev1])),[member1 of v0],[v1]),[term_of(member1)],[member1])),[v1,v0,v2,lambda(v3,su(su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of lambda(v3,su(lambda(v4,su(su(su(lambda(v5,su(decide(v6,[v8,su(su(su(su(su(su(su(v12,[v11 of v7],[v12]),[v9 of lambda(v11,spread(v11,[v12,v13,su(v15,[v12 of v8],[v15])]))],[v11]),[v13 of member(v3,app(rev(v0),v1::nil))],[v9]),[v12 of member(v3,app(rev(v0),v1::nil))],[v13]),[v11 of member(v3,v1::nil)],[v12]),[v9 of member(v3,rev(v0))],[v11]),[term_of(ipc_dp_imp_e3)],[v9])],[v9,su(su(su(su(su(su(su(v12,[v10 of v7],[v12]),[v8 of lambda(v10,spread(v10,[v12,v13,su(v15,[v13 of v9],[v15])]))],[v10]),[v13 of member(v3,app(rev(v0),v1::nil))],[v8]),[v12 of member(v3,app(rev(v0),v1::nil))],[v13]),[v10 of member(v3,v1::nil)],[v12]),[v8 of member(v3,rev(v0))],[v10]),[term_of(ipc_dp_imp_e3)],[v8])]),[v4 of v5],[v6])),[v6 of(v1::nil)],[v7]),[v5 of rev(v0)],[v6]),[memapp3 of v3],[v5]))of(lambda(v4,su(v5,[v4 of v3],[v5]))of lambda(x,lambda(v4,decide(v4,[v5,lambda(v3,su(su(su(su(su(lambda(v4,su(lambda(v6,inl(su(decide(v7,[v8,su(v9,[v5 of v8],[v9])],[v9,su(v8,[v5 of v6],[v8])]),[v4 of v6],[v7]))),[v2 of x],[v5]))of su(su(su(su(su(su(su(lambda(v4,inl(v4)),[member1 of x],[v4]),[term_of(member1)],[member1]),[v6 of v3],[v4]),[v5 of nil],[v6]),[v4 of v1],[v5]),[member3 of x],[v4]),[term_of(member3)],[member3]),[v6 of v3],[v4]),[v5 of v0],[v6]),[v4 of v1],[v5]),[member3 of x],[v4]),[term_of(member3)],[member3]))of v5],[v6,lambda(v3,su(su(su(su(su(_131291,[v6 of v3],[v4]),[v5 of v0],[v6]),[v4 of v1],[v5]),[member2 of x],[v4]),[term_of(member2)],[member2]))of v6]))of su(su(su(v5,[v4 of v1],[v5]),[v3 of x],[v4]),[term_of(deceqint)],[v3]))),[term_of(memapp3)],[memapp3])),[v4 of v0],[v5]),[rev2 of v1],[v4]),[term_of(rev2)],[rev2]))])))),
[problem([y:int list,v1:int,v0:int list,v2:x:int=>member(x,v0)=>member(x,rev(v0)),x:int,v3:x=v1 in int]==>{true}=>member(x,rev(v0))\member(x,v1::nil),
 sym_eval(equal(v3,right)then[normalize_term([reduction([2,2],[member2,equ(u(1),left)])])])then[elementary(intro(new[v3])then[intro(right)then[hyp(v3),wfftacs],wfftacs])],su(su(su(su(su(lambda(v3,inr(v3)),[v5 of axiom],[v3]),[v4 of nil],[v5]),[v3 of v1],[v4]),[member2 of v1],[v3]),[term_of(member2)],[member2]),
 [
 ]) ext _131291
]).
