problem([]==>n:pnat=>half(double(n))=n in pnat,
ind_strat(induction(lemma(pnat_primitive)-[(n:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[double1,equ(pnat,left)]),reduction([1,1],[half1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,1,1],[double2,equ(pnat,left)],[])then[wave(direction_out,[1,1],[half3,equ(pnat,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,[1],v1)]))then elementary(identity)))])]),lambda(n,p_ind(n,su(su(axiom,[term_of(half1)],[half1]),[term_of(double1)],[double1]),[v0,v1,su(su(su(su(axiom,[half3 of double(v0)],[v2]),[term_of(half3)],[half3]),[double2 of v0],[v2]),[term_of(double2)],[double2])])),
[
]).
