proposition: Lemma ord_negl_pint a b n : natp n -> ordinalp a -> ordinalp b -> a <<o b -> a *o n <<o b.
proof: Proof. move => nN oa ob H; move: n nN. apply:Nat_induction; first by rewrite oprod0r /ord_negl (osum0l ob). move => n nN Hr; rewrite (succ_of_nat nN) (oprod2_succ oa (OS_nat nN)). by apply/(ord_negl_sum1 (OS_prod2 oa (OS_nat nN)) oa ob). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)