problem([]==>x:pnat=>y:pnat=>minus(x,y)=minus(s(x),s(y))in pnat,
sym_eval(normalize_term([reduction([2,1],[minus2,equ(pnat,left)])])),lambda(v0,lambda(v1,su(su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of _174760,[v2 of v1],[v3]),[minus2 of s(v0)],[v2]),[term_of(minus2)],[minus2]))),
[problem([]==>x:pnat=>y:pnat=>minus(x,y)=pred(minus(s(x),y))in pnat,
 ind_strat(induction(lemma(pnat_primitive)-[(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[minus1,equ(pnat,left)]),reduction([1,2,1],[minus1,equ(pnat,left)]),reduction([2,1],[pred2,equ(pnat,left)])]))then[elementary(intro(new[x])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[minus2,equ(pnat,left)],[])then[wave(direction_out,[1,2,1],[minus2,equ(pnat,left)],[])then[unblock_then_wave(direction_out,unblock_lazy([unblock(meta_ripple,unused,unused),idtac])then wave(direction_out,[],[cnc_pred,imp(right)],[]))]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])]),lambda(v0,lambda(v1,lambda(v2,su(su(v4,[v3 of v0],[v4]),[v2 of v1],[v3]))of lambda(y,p_ind(y,lambda(v0,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(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(x,axiom),[pred2 of v0],[v1]),[term_of(pred2)],[pred2])),[minus1 of s(v0)],[v1]),[term_of(minus1)],[minus1])),[minus1 of v0],[v1]),[term_of(minus1)],[minus1])),[v0,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(su(su(v3,[v4 of(lambda(v3,su(v4,[v3 of v2],[v4]))of v1)],[v3]),[v3 of pred(minus(s(v2),v0))],[v4]),[cnc_pred of minus(v2,v0)],[v3]),[term_of(cnc_pred)],[cnc_pred])),[v3 of v0],[v4]),[minus2 of s(v2)],[v3]),[term_of(minus2)],[minus2])),[v3 of v0],[v4]),[minus2 of v2],[v3]),[term_of(minus2)],[minus2]))])))),
 [
 ]) ext _174760
]).
