proposition: Lemma oprod_Meqle a b c: a <=o b -> ordinalp c -> (c *o a) <=o (c *o b).
proof: Proof. move => ab oc. case: (ozero_dichot oc) => cz. rewrite cz oprod0l oprod0l; apply: (oleR OS0). case: (equal_or_not a b) => nab. by rewrite nab; apply: oleR; apply: (OS_prod2 oc (proj32 ab)). exact: (proj1 (oprod_Meqlt (conj ab nab) cz)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)