proposition: Lemma compare_succ_r p q : switch_Eq Gt (p ?= succ q) = switch_Eq Lt (p ?= q).
proof: Proof. revert q. induction p as [p IH|p IH| ]; intros [q|q| ]; simpl; simpl_compare; rewrite ?IH; trivial; (now destruct compare) || (now destruct p). Qed.
imports: BinNums Eqdep_dec EqdepFacts RelationClasses Morphisms Setoid Equalities Orders OrdersFacts GenericMinMax PeanoNat BinPosDef