problem([]==>a:pnat=>b:pnat=>leq(a,b)\leq(b,a),
ind_strat(induction(lemma(pairs)-[(a:pnat)-s(v1),(b:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1],[leq1,equ(u(1),left)])]))then[elementary(intro(left)then[istrue,wfftacs])]),base_case(sym_eval(normalize_term([reduction([2],[leq1,equ(u(1),left)])]))then[elementary(intro(right)then[istrue,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2],[leq3,equ(u(1),left)],[])then[wave(direction_out,[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(a,lambda(b,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]),[leq3 of v0],[v3]),[term_of(leq3)],[leq3]))))],[v10]),[v8 of lambda(v0,su(su(inr(0),[leq1 of v0],[v1]),[term_of(leq1)],[leq1]))],[v9]),[v7 of lambda(v0,su(su(inl(0),[leq1 of v0],[v1]),[term_of(leq1)],[leq1]))],[v8]),[v6 of b],[v7]),[v5 of a],[v6]),[v3 of lambda(a,lambda(b,leq(a,b)\leq(b,a)))],[v5]))of v4,[term_of(pairs)],[v4]))))))),
[
]).
