intros f1 f2 H' H'0 H'1 H'2; red in |- *.
rewrite
FcanonicUnique
with
(3 := pGivesBound)
(p := Fnormalize radix b precision f2)
(q := Fnormalize radix b precision f1);
auto with float arith.
repeat rewrite FnormalizeCorrect; auto.
Qed.

Theorem FNevenEq :
forall f1 f2 : float,
Fbounded b f1 -> Fbounded b f2 -> f1 = f2 :>R -> FNeven f1 -> FNeven f2.