problem([]==>n:pnat=>even(n)=>double(half(n))=n in pnat,
ind_strat(induction(lemma(twos)-[(n:pnat)-s(s(v0))])then[base_case(sym_eval(normalize_term([reduction([1],[even1,equ(u(1),left)]),reduction([1,1,1,2],[half1,equ(pnat,left)]),reduction([1,1,2],[double1,equ(pnat,left)])]))then[elementary(intro(new[v0])then[identity,wfftacs])]),base_case(sym_eval(normalize_term([reduction([1],[even2,equ(u(1),left)]),reduction([1,1,1,2],[half2,equ(pnat,left)]),reduction([1,1,2],[double1,equ(pnat,left)])]))then[elementary(intro(new[v0])then[elim(v0),wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1],[even3,equ(u(1),left)],[])then[wave(direction_out,[1,1,1,2],[half3,equ(pnat,left)],[])then[wave(direction_out,[1,1,2],[double2,equ(pnat,left)],[])then[wave(direction_out,[2],[cnc_s,imp(right)],[])then[wave(direction_out,[2],[cnc_s,imp(right)],[])]]]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])]),lambda(n,su(lambda(v3,su(su(su(su(su(v8,[v7 of n],[v8]),[v6 of lambda(v0,lambda(v1,su(su(su(su(su(su(su(lambda(v2,su(su(lambda(v3,su(su(su(v7,[v4 of v6],[v7]),[v2 of v3],[v6]),[v1 of v3],[v5])),[v3 of s(v0)],[v4]),[cnc_s of s(double(half(v0)))],[v3]))of su(lambda(v2,su(su(lambda(v3,su(su(su(v7,[v4 of v6],[v7]),[v2 of v3],[v6]),[v1 of v3],[v5])),[v3 of v0],[v4]),[cnc_s of double(half(v0))],[v3]))of v1,[term_of(cnc_s)],[cnc_s]),[term_of(cnc_s)],[cnc_s]),[double2 of half(v0)],[v2]),[term_of(double2)],[double2]),[half3 of v0],[v2]),[term_of(half3)],[half3]),[even3 of v0],[v2]),[term_of(even3)],[even3])))],[v7]),[v5 of su(su(su(lambda(v0,any(v0)),[term_of(double1)],[double1]),[term_of(half2)],[half2]),[term_of(even2)],[even2])],[v6]),[v4 of su(su(su(lambda(v0,axiom),[term_of(double1)],[double1]),[term_of(half1)],[half1]),[term_of(even1)],[even1])],[v5]),[v3 of lambda(n,even(n)=>double(half(n))=n in pnat)],[v4]))of v2,[term_of(twos)],[v2])),
[
]).
