proposition: Lemma sub_lt_mono_l p q r: q<p -> p<r -> r-p < r-q.
proof: Proof. intros Hqp Hpr. apply (add_lt_mono_r p). rewrite sub_add by trivial. apply le_lt_trans with ((r-q)+q). - rewrite sub_add by (now apply lt_trans with p). apply le_refl. - now apply add_lt_mono_l. Qed.
imports: BinNums Eqdep_dec EqdepFacts RelationClasses Morphisms Setoid Equalities Orders OrdersFacts GenericMinMax PeanoNat BinPosDef