intros P r q H' H'0.
case H'.
intros H'1 H'2; elim H'2; intros H'3 H'4; elim H'4; intros H'5 H'6;
case H'5 with (1 := H'0); clear H'4 H'2; intros H;
case H; auto.
Qed.

Theorem RoundedModeProjectorIdemEq :
forall (P : R -> float -> Prop) (p q : float),
RoundedModeP b radix P -> Fbounded b p -> P (FtoR radix p) q -> p = q :>R.