problem([]==>x:pnat=>y:pnat=>z:pnat=>less(x,y)=>less(x,plus(y,z)),
ind_strat(induction(lemma(pnat_primitive)-[(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1],[less1,equ(u(1),left)]),reduction([2,2],[plus1,equ(pnat,left)])]))then[elementary(intro(new[x])then[intro(new[z])then[intro(new[v0])then[elim(v0),wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,2],[plus2,equ(pnat,left)],[]))then[idtac])]),lambda(v0,lambda(v1,lambda(v2,lambda(v3,su(su(su(v6,[v5 of v2],[v6]),[v4 of v0],[v5]),[v3 of v1],[v4]))of lambda(y,p_ind(y,lambda(v0,lambda(v1,su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of lambda(v0,lambda(v1,su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of lambda(x,lambda(z,lambda(v0,any(v0)))),[plus1 of v1],[v2]),[term_of(plus1)],[plus1]))),[less1 of v0],[v2]),[term_of(less1)],[less1]))),[v0,v1,lambda(v2,lambda(v3,su(su(su(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of _208333,[v4 of v3],[v5]),[plus2 of v0],[v4]),[term_of(plus2)],[plus2])))]))))),
[problem([y:pnat,v0:pnat,v1:x:pnat=>z:pnat=>less(x,v0)=>less(x,plus(v0,z))]==>x:pnat=>z:pnat=>less(x,s(v0))=>less(x,s(plus(v0,z))),
 ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v2)])then[base_case(sym_eval(normalize_term([reduction([1],[less2,equ(u(1),left)]),reduction([2],[less2,equ(u(1),left)])]))then[elementary(intro(new[z])then[intro(new[v2])then[hyp(v2),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2],[less3,equ(u(1),left)],[])then[wave(direction_out,[1],[less3,equ(u(1),left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])]),lambda(x,p_ind(x,lambda(v2,su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(z,lambda(v2,v2)),[less2 of plus(v0,v2)],[v3]),[term_of(less2)],[less2])),[less2 of v0],[v3]),[term_of(less2)],[less2])),[v2,v3,lambda(v4,su(su(su(lambda(v5,su(v6,[v5 of v4],[v6]))of lambda(v4,su(su(su(lambda(v5,su(v6,[v5 of v4],[v6]))of lambda(z,su(su(v5,[v4 of z],[v5]),[v1 of v2],[v4])),[v5 of v0],[v6]),[less3 of v2],[v5]),[term_of(less3)],[less3])),[v5 of plus(v0,v4)],[v6]),[less3 of v2],[v5]),[term_of(less3)],[less3]))])),
 [
 ]) ext _208333
]).
