proposition: Lemma R_mult_dist_minus : forall x y z, R_mult x (y[-]z) [=] R_mult x y[-]R_mult x z.
proof: Proof. intros x y z H. elim H; intro Hlt; elim Hlt; intros N HN; elim HN; clear H Hlt HN; intros e He HN; simpl in HN; apply (less_irreflexive_unfolded _ e). eapply leEq_less_trans. apply (HN N (le_n _)). rstepl ([0]:F); auto. eapply leEq_less_trans. apply (HN N (le_n _)). rstepl ([0]:F); auto. Qed.
imports: CoRN.algebra.COrdCauchy CoRN.tactics.RingReflection