problem([]==>x:pnat=>y:pnat=>geq(x,y)=>less(x,y)=>void,
ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1],[geqzero,equiv(left)]),reduction([1,2],[lesszero,equiv(left)])]))then[elementary(intro(new[v1])then[intro(new[v2])then[elim(v2)then[hyp(v1),hyp(v3)],wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([1],[geq1,equ(u(1),left)]),reduction([1,2],[less1,equ(u(1),left)])]))then[elementary(intro(new[v1])then[intro(new[v2])then[hyp(v2),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1],[geq3,equ(u(1),left)],[])then[wave(direction_out,[1,2],[less3,equ(u(1),left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2))])]),lambda(v0,lambda(v1,lambda(v2,su(su(v4,[v3 of v0],[v4]),[v2 of v1],[v3]))of lambda(v0,lambda(v1,lambda(v2,su(su(v4,[v3 of v0],[v4]),[v2 of v1],[v3]))of lambda(x,lambda(y,su(lambda(v3,su(su(su(su(su(su(v10,[v9 of lambda(v1,lambda(v0,lambda(v2,su(su(su(su(su(su(v2,[v3 of v0],[v4]),[less3 of v1],[v3]),[term_of(less3)],[less3]),[v3 of v0],[v4]),[geq3 of v1],[v3]),[term_of(geq3)],[geq3]))))],[v10]),[v8 of lambda(v0,su(su(su(su(lambda(v1,lambda(v2,v2)),[less1 of v0],[v1]),[term_of(less1)],[less1]),[geq1 of v0],[v1]),[term_of(geq1)],[geq1]))],[v9]),[v7 of lambda(v0,su(su(spread(v1,[v2,v3,lambda(v5,lambda(v6,su(v7,[v5 of su(v7,[v2 of v6],[v7])],[v7])))of su(su(spread(v1,[v2,v3,lambda(v5,lambda(v6,su(lambda(v8,su(v9,[v7 of su(v9,[v2 of v8],[v9])],[v9])),[v5 of v6],[v7])))of lambda(v1,lambda(v2,su(v3,[v2 of v1],[v3])))]),[lesszero of v0],[v1]),[term_of(lesszero)],[lesszero])]),[geqzero of v0],[v1]),[term_of(geqzero)],[geqzero]))],[v8]),[v6 of y],[v7]),[v5 of x],[v6]),[v3 of lambda(x,lambda(y,geq(x,y)=>less(x,y)=>void))],[v5]))of v4,[term_of(pairs)],[v4]))))))),
[
]).
