proposition: Lemma add_carry_add p q r s : add_carry p r = add_carry q s -> p + r = q + s.
proof: Proof. intros H; apply succ_inj; now rewrite <- 2 add_carry_spec. Qed.
imports: BinNums Eqdep_dec EqdepFacts RelationClasses Morphisms Setoid Equalities Orders OrdersFacts GenericMinMax PeanoNat BinPosDef