proposition: Lemma oppe_subset (A B : set (\bar R)) : ((A `<=` B) <-> (-%E @` A `<=` -%E @` B))%classic.
proof: Proof. split=> [AB _ [] x ? <-|AB x Ax]; first by exists x => //; exact: AB. have /AB[y By] : ((-%E @` A) (- x))%classic by exists x. by rewrite eqe_oppP => <-. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(fsbigop cardinality set_interval) reals signed topology constructive_ereal