Definition is_finite f :=
match f with
| B754_finite _ _ _ _ => true
| B754_zero _ => true
| _ => false
end.
Definition is_finite_FF f :=
match f with
| F754_finite _ _ _ => true
| F754_zero _ => true
| _ => false
end.

(* Specifications: *)
Theorem is_finite_FF2B :
forall x Hx,
is_finite (FF2B x Hx) = is_finite_FF x.
Theorem is_finite_FF_B2FF :
forall x,
is_finite_FF (B2FF x) = is_finite x.
Theorem B2R_Bsign_inj:
forall x y : binary_float,
is_finite x = true ->
is_finite y = true ->
B2R x = B2R y ->
Bsign x = Bsign y ->
x = y.
Theorem is_finite_FF2B :
forall x Hx,
is_finite (FF2B x Hx) = is_finite_FF x.
Theorem is_finite_FF_B2FF :
forall x,
is_finite_FF (B2FF x) = is_finite x.
Theorem B2R_Bsign_inj:
forall x y : binary_float,
is_finite x = true ->
is_finite y = true ->
B2R x = B2R y ->
Bsign x = Bsign y ->
x = y.