proposition: Theorem add_mibs : forall a b c d : R, forall zi : FF, BND ((a - c) + (b - d)) zi -> BND ((a + b) - (c + d)) zi.
proof: Proof. intros a b c d zi Hz. replace ((a + b) - (c + d))%R with ((a - c) + (b - d))%R. exact Hz. ring. Qed.
imports: Reals Gappa_common