(** Compatibility with subtraction *)

Remark Zfloor_minus:
  forall x n, Zfloor (x - Z2R n) = Zfloor x - n.

(* Specifications: *)
Theorem ZofB_minus: forall minus_nan m f p q, ZofB f = Some p -> 0 <= p < 2*q -> q <= 2^prec -> (Z2R q <= B2R _ _ f)%R -> ZofB (Bminus _ _ _ Hmax minus_nan m f (BofZ q)) = Some (p - q).
Theorem ZofB_minus: forall minus_nan m f p q, ZofB f = Some p -> 0 <= p < 2*q -> q <= 2^prec -> (Z2R q <= B2R _ _ f)%R -> ZofB (Bminus _ _ _ Hmax minus_nan m f (BofZ q)) = Some (p - q).