(** Bitwise operations and arithmetical operations *)
Local Notation xor3 a b c := (xorb (xorb a b) c).
Local Notation lxor3 a b c := (lxor (lxor a b) c).
Local Notation nextcarry a b c := ((a&&b) || (c && (a||b))).
Local Notation lnextcarry a b c := (lor (land a b) (land c (lor a b))).

Lemma add3_bit0 : forall a b c,
(a+b+c).[0] = xor3 a.[0] b.[0] c.[0].