Section Fcore_generic_round_pos.
(** Rounding functions: R -> Z *)
Variable rnd : R -> Z.
Class Valid_rnd := {
Zrnd_le : forall x y, (x <= y)%R -> (rnd x <= rnd y)%Z ;
Zrnd_IZR : forall n, rnd (IZR n) = n
}.
Context { valid_rnd : Valid_rnd }.
(** the most useful one: R -> F *)
Definition round x :=
F2R (Float beta (rnd (scaled_mantissa x)) (cexp x)).
End Fcore_generic_round_pos.

Theorem round_ext :
forall rnd1 rnd2,
( forall x, rnd1 x = rnd2 x ) ->
forall x,
round rnd1 x = round rnd2 x.