problem([]==>x:pnat=>y:pnat=>((x=y in pnat=>void)#leq(x,y))=>less(x,y),
ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1],[leq1,equ(u(1),left)]),reduction([2],[lesszero,equiv(left)])]))then[elementary(intro(new[v1])then[intro(new[v2])then[elim(v1)then elim(v3)then[hyp(v2),hyp(v6)],wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([2,1],[leqzero,equiv(left)]),reduction([2],[less1,equ(u(1),left)])]))then[elementary(intro(new[v1])then[elim(v1)then elim(v2)then[hyp(v3),hyp(v5)],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2],[less3,equ(u(1),left)],[])then[wave(direction_out,[2,1],[leq3,equ(u(1),left)],[])then[wave(direction_out,[1,1,1],[cnc_s,imp(right)],[])]])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(su(lambda(v3,su(su(lambda(v4,su(v6,[v3 of spread(v4,[v6,v7,lambda(v9,su(v10,[v6 of su(v10,[v5 of v9],[v10])],[v10]))&v7])],[v6])),[v4 of v0],[v5]),[cnc_s of v1],[v4]))of v2,[term_of(cnc_s)],[cnc_s]),[v3 of v0],[v4]),[leq3 of v1],[v3]),[term_of(leq3)],[leq3]),[v3 of v0],[v4]),[less3 of v1],[v3]),[term_of(less3)],[less3]))))],[v10]),[v8 of lambda(v0,su(su(spread(v1,[v2,v3,lambda(v5,lambda(v6,su(v7,[v5 of spread(v6,[v7,v8,v7&su(v10,[v2 of v8],[v10])])],[v7])))of su(su(lambda(v1,spread(v1,[v2,v3,su(v5,[v2 of v3],[v5])])),[less1 of v0],[v1]),[term_of(less1)],[less1])]),[leqzero of v0],[v1]),[term_of(leqzero)],[leqzero]))],[v9]),[v7 of lambda(v0,su(su(su(su(spread(v1,[v2,v3,lambda(v5,lambda(v6,spread(v6,[v7,v8,spread(v1,[v10,v11,su(su(su(su(su(su(su(v15,[v14 of v11],[v15]),[v13 of(lambda(v14,v14)&lambda(v14,lambda(v15,su(su(su(su(su(su(su(v18,[v17 of v3],[v18]),[v16 of(lambda(v17,su(su(v19,[v18 of v15],[v19]),[v10 of v17],[v18]))&lambda(v17,lambda(v18,su(su(su(su(su(su(su(v21,[v20 of v5],[v21]),[v19 of lambda(v20,su(su(su(su(su(su(su(v23,[v22 of v20],[v23]),[v21 of(lambda(v22,su(su(v24,[v23 of v18],[v24]),[v22 of v8],[v23]))&lambda(v22,v7))],[v22]),[v24 of void],[v21]),[v23 of(0=v0 in pnat)],[v24]),[v22 of({true}=>v0=0 in pnat=>void)],[v23]),[v21 of void],[v22]),[term_of(ipc_dp_imp_e4)],[v21]))],[v20]),[v22 of void],[v19]),[v21 of(v0=0 in pnat=>void)],[v22]),[v20 of{true}],[v21]),[v19 of(0=v0 in pnat=>void)],[v20]),[term_of(ipc_dp_imp_e2)],[v19]))))],[v17]),[v19 of void],[v16]),[v18 of(v0=0 in pnat)],[v19]),[v17 of less(0,v0)],[v18]),[v16 of void],[v17]),[term_of(ipc_dp_imp_e4)],[v16]))))],[v14]),[v16 of void],[v13]),[v15 of(v0=0 in pnat)],[v16]),[v14 of less(0,v0)],[v15]),[v13 of less(0,v0)],[v14]),[term_of(ipc_dp_imp_e4)],[v13])])])))of lambda(v1,lambda(v2,spread(v1,[v3,v4,su(v6,[v3 of v2],[v6])])))]),[lesszero of v0],[v1]),[term_of(lesszero)],[lesszero]),[leq1 of v0],[v1]),[term_of(leq1)],[leq1]))],[v8]),[v6 of y],[v7]),[v5 of x],[v6]),[v3 of lambda(x,lambda(y,((x=y in pnat=>void)#leq(x,y))=>less(x,y)))],[v5]))of v4,[term_of(pairs)],[v4]))))))),
[
]).
