proposition: Lemma oprec_Mlt a b: \0o <o a -> a <o b -> (a -o \1o) <o (b -o \1o).
proof: Proof. move => ap ab. have [[oa ob _] _ ] := ab. case: (oleT_el OS_omega oa) => af. by rewrite (odiff_1inf af) (odiff_1inf (oleT af (proj1 ab))). case: (oleT_el OS_omega ob) => bf. rewrite (odiff_1inf bf); apply: olt_leT bf. exact: (ole_ltT (odiff_Mle OS1 oa) af). apply /oltSSP. by rewrite - (oprec_nat ap af) - (oprec_nat (olt_leT ap (proj1 ab)) bf). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)