problem([]==>x:pnat=>y:pnat=>(even(x)#even(y))=>even(plus(x,y)),
ind_strat(induction(lemma(twos)-[(x:pnat)-s(s(v0))])then[base_case(sym_eval(normalize_term([reduction([1,1],[even1,equ(u(1),left)]),reduction([1,2],[plus1,equ(pnat,left)])]))then[elementary(intro(new[y])then[intro(new[v0])then[elim(v0)then hyp(v2),wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([1,1],[even2,equ(u(1),left)]),reduction([1,2],[plus2,equ(pnat,left)]),reduction([1,1,2],[plus1,equ(pnat,left)])]))then[elementary(intro(new[y])then[intro(new[v0])then[elim(v0)then elim(v1),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1,2],[plus2,equ(pnat,left)],[])then[wave(direction_out,[2],[even3,equ(u(1),left)],[])then[wave(direction_out,[1,1],[even3,equ(u(1),left)],[])]]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])]),lambda(x,su(lambda(v3,su(su(su(su(su(v8,[v7 of x],[v8]),[v6 of lambda(v0,lambda(v1,lambda(v2,su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(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 v1,[even3 of v0],[v3]),[term_of(even3)],[even3])),[even3 of plus(v0,v2)],[v3]),[term_of(even3)],[even3])),[v3 of v2],[v4]),[plus2 of v0],[v3]),[term_of(plus2)],[plus2])),[v3 of v2],[v4]),[plus2 of s(v0)],[v3]),[term_of(plus2)],[plus2]))))],[v7]),[v5 of lambda(v0,su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(y,lambda(v0,spread(v0,[v1,v2,any(v1)]))),[plus1 of v0],[v1]),[term_of(plus1)],[plus1])),[v1 of v0],[v2]),[plus2 of 0],[v1]),[term_of(plus2)],[plus2])),[term_of(even2)],[even2]))],[v6]),[v4 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(y,lambda(v0,spread(v0,[v1,v2,v2]))),[plus1 of v0],[v1]),[term_of(plus1)],[plus1])),[term_of(even1)],[even1]))],[v5]),[v3 of lambda(x,y:pnat=>(even(x)#even(y))=>even(plus(x,y)))],[v4]))of v2,[term_of(twos)],[v2])),
[
]).
