problem([]==>x:pnat=>y:pnat=>(leq(x,y)=>void)=>less(y,x),
ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[leq1,equ(u(1),left)]),reduction([2],[less1,equ(u(1),left)])]))then[elementary(intro(new[v1])then[elim(v1)then[istrue,hyp(v2)],wfftacs])]),base_case(sym_eval(normalize_term([reduction([1,1],[leqzero,equiv(left)]),reduction([2],[lesszero,equiv(left)])]))then[elementary(intro(new[v1])then[hyp(v1),wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2],[less3,equ(u(1),left)],[])then[wave(direction_out,[1,1],[leq3,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]),[leq3 of v1],[v3]),[term_of(leq3)],[leq3]),[v3 of v1],[v4]),[less3 of v0],[v3]),[term_of(less3)],[less3]))))],[v10]),[v8 of lambda(v0,su(su(spread(v1,[v2,v3,lambda(v5,lambda(v6,su(v7,[v5 of lambda(v7,su(v8,[v6 of su(v8,[v3 of v7],[v8])],[v8]))],[v7])))of su(su(spread(v1,[v2,v3,lambda(v5,v3)of lambda(v1,v1)]),[lesszero of v0],[v1]),[term_of(lesszero)],[lesszero])]),[leqzero of v0],[v1]),[term_of(leqzero)],[leqzero]))],[v9]),[v7 of lambda(v0,su(su(su(su(lambda(v1,su(v2,[v1 of 0],[v2])),[less1 of v0],[v1]),[term_of(less1)],[less1]),[leq1 of v0],[v1]),[term_of(leq1)],[leq1]))],[v8]),[v6 of y],[v7]),[v5 of x],[v6]),[v3 of lambda(x,lambda(y,(leq(x,y)=>void)=>less(y,x)))],[v5]))of v4,[term_of(pairs)],[v4]))))))),
[
]).
