proposition: Lemma add_diag p : p + p = p~0.
proof: Proof. induction p as [p IHp| p IHp| ]; simpl; now rewrite ?add_carry_spec, ?IHp. Qed.
imports: BinNums Eqdep_dec EqdepFacts RelationClasses Morphisms Setoid Equalities Orders OrdersFacts GenericMinMax PeanoNat BinPosDef