problem([]==>a:int list=>b:int list=>c:int list=>f:(int=>int list=>int list)=>lit(app(a,b),c,f)=lit(a,lit(b,c,f),f)in int list,
ind_strat(induction(lemma(list_primitive)-[(a:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[app1,equ(int list,left)]),reduction([2,1],[lit1,equ(int list,left)])]))then[elementary(intro(new[b])then[intro(new[c])then[intro(new[f])then[identity,wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,1],[lit2,equ(int list,left)],[])then[wave(direction_out,[1,1,1],[app2,equ(int list,left)],[])then[wave(direction_out,[1,1],[lit2,equ(int list,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],v2)]))then elementary(intro(new[b])then[intro(new[c])then[intro(new[f])then[identity,wfftacs],wfftacs],wfftacs])))])]),lambda(a,list_ind(a,lambda(v0,lambda(v1,lambda(v2,su(su(lambda(v3,su(su(su(v6,[v5 of v2],[v6]),[v4 of v1],[v5]),[v3 of v0],[v4]))of lambda(v0,lambda(v1,lambda(v2,su(su(su(lambda(v3,su(su(su(v6,[v5 of v2],[v6]),[v4 of v1],[v5]),[v3 of v0],[v4]))of lambda(b,lambda(c,lambda(f,axiom))),[v3 of v2],[v4]),[lit1 of lit(v0,v1,v2)],[v3]),[term_of(lit1)],[lit1])))),[app1 of v0],[v3]),[term_of(app1)],[app1])))),[v1,v0,v2,lambda(v3,lambda(v4,lambda(v5,su(su(su(su(su(lambda(v6,su(su(su(v9,[v8 of v5],[v9]),[v7 of v4],[v8]),[v6 of v3],[v7]))of lambda(v3,lambda(v4,lambda(v5,su(su(su(su(lambda(v6,su(su(su(v9,[v8 of v5],[v9]),[v7 of v4],[v8]),[v6 of v3],[v7]))of lambda(v3,lambda(v4,lambda(v5,su(su(su(su(su(lambda(v6,su(su(su(v9,[v8 of v5],[v9]),[v7 of v4],[v8]),[v6 of v3],[v7]))of lambda(v3,lambda(v4,lambda(v5,su(su(su(axiom,[v7 of v5],[v8]),[v6 of v4],[v7]),[v2 of v3],[v6])))),[v8 of v5],[v9]),[v7 of v4],[v8]),[v6 of app(v0,v3)],[v7]),[lit2 of v1],[v6]),[term_of(lit2)],[lit2])))),[v7 of v3],[v8]),[v6 of v0],[v7]),[app2 of v1],[v6]),[term_of(app2)],[app2])))),[v8 of v5],[v9]),[v7 of lit(v3,v4,v5)],[v8]),[v6 of v0],[v7]),[lit2 of v1],[v6]),[term_of(lit2)],[lit2]))))])),
[
]).
