proposition: Lemma addcarries_lor_land x y : addcarries (x .| y) (x .& y) = addcarries x y.
proof: Proof. apply Z.bits_inj'; refine (Wf_Z.natlike_ind _ _ _); [prove_bitwise|intros i??]. rewrite 2 (testbit_addcarries_pos _ _ (Z.succ i)) by lia; replace (Z.succ i-1) with i by lia; prove_bitwise. Qed.
imports: BinInt Lia Btauto