proposition: Lemma infsN u : infs (-%R \o u) = - sups u.
proof: Proof. apply/eqP; rewrite -eqr_oppLR -supsN; apply/eqP; congr (sups _). by rewrite funeqE => ? /=; rewrite opprK. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(set_interval) reals ereal signed topology normedtype landau