proposition: Lemma contract_inf S : S !=set0 -> contract (ereal_inf S) = inf (contract @` S).
proof: Proof. move=> -[x Sx]; rewrite /ereal_inf /contract (contractN (ereal_sup (-%E @` S))). by rewrite -/contract contract_sup /inf; [rewrite contract_imageN | exists (- x), x]. 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