intros P H' p q H'0.
apply MinOrMaxRep with (P := P); auto with inv.
Qed.
Definition SymmetricP (P : R -> float -> Prop) :=
forall (r : R) (p : float), P r p -> P (- r)%R (Fopp p).

(* Specifications: *)
Theorem ToZeroSymmetric : SymmetricP ToZeroP.
red in |- *; intros r p H'; case H'; clear H'; intros H'; case H';
intros H'1 H'2.