intros r1 r2 p q H'; case H'.
intros H'0 H'1 H'2; left; split;
try apply MinCompatible with (p := p) (r1 := r1);
try rewrite <- H'1; auto; case H'0; auto.
intros H'0 H'1 H'2; right; split;
try apply MaxCompatible with (p := p) (r1 := r1);
try rewrite <- H'1; auto; case H'0; auto.
Qed.

(* Specifications: *)
Theorem ToZeroMinOrMax : MinOrMaxP ToZeroP.
red in |- *.