problem([]==>x:pnat=>less(0,fac(x)),
ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2],[fac1,equ(pnat,left)]),reduction([],[less2,equ(u(1),left)])]))then[elementary(istrue)]),step_case(ripple(direction_out,wave(direction_out,[2],[fac2,equ(pnat,left)],[])then[wave(direction_out,[],[times_less,imp(right)],[])])then[idtac])]),lambda(x,p_ind(x,su(su(su(0,[less2 of 0],[v0]),[term_of(less2)],[less2]),[term_of(fac1)],[fac1]),[v0,v1,su(su(su(su(su(su(v2,[v3 of _744],[v2]),[v2 of fac(v0)],[v3]),[times_less of s(v0)],[v2]),[term_of(times_less)],[times_less]),[fac2 of v0],[v2]),[term_of(fac2)],[fac2])])),
[problem([x:pnat,v0:pnat,v1:less(0,fac(v0))]==>less(0,s(v0))#less(0,fac(v0)),
 sym_eval(normalize_term([reduction([1],[less2,equ(u(1),left)])]))then[elementary(intro then[istrue,hyp(v1)])],su(su(0&v1,[less2 of v0],[v2]),[term_of(less2)],[less2]),
 [
 ]) ext _744
]).
