problem([]==>x:pnat=>odd(x)=>even(x)=>void,
ind_strat(induction(lemma(twos)-[(x:pnat)-s(s(v0))])then[base_case(sym_eval(normalize_term([reduction([1],[odd1,equ(u(1),left)]),reduction([1,2],[even1,equ(u(1),left)])]))then[elementary(intro(new[v0])then[elim(v0),wfftacs])]),base_case(sym_eval(normalize_term([reduction([1],[odd2,equ(u(1),left)]),reduction([1,2],[even2,equ(u(1),left)])]))then[elementary(intro(new[v0])then[intro(new[v1])then[hyp(v1),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1],[odd3,equ(u(1),left)],[])then[wave(direction_out,[1,2],[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,su(su(su(su(v1,[even3 of v0],[v2]),[term_of(even3)],[even3]),[odd3 of v0],[v2]),[term_of(odd3)],[odd3])))],[v7]),[v5 of su(su(lambda(v0,lambda(v1,v1)),[term_of(even2)],[even2]),[term_of(odd2)],[odd2])],[v6]),[v4 of su(su(lambda(v0,any(v0)),[term_of(even1)],[even1]),[term_of(odd1)],[odd1])],[v5]),[v3 of lambda(x,odd(x)=>even(x)=>void)],[v4]))of v2,[term_of(twos)],[v2])),
[
]).
