intros (m1,e1).
apply F2R_Zabs.
Qed.
Definition Fplus (f1 f2 : float beta) : float beta :=
let '(m1, m2 ,e) := Falign f1 f2 in
Float (m1 + m2) e.

Theorem Fplus_same_exp :
forall m1 m2 e,
Fplus (Float m1 e) (Float m2 e) = Float (m1 + m2) e.