proposition: Lemma continuous_subspace_itv (I : interval R) (f : R -> R) : {in I, continuous f} -> {within [set` I], continuous f}.
proof: Proof. move=> ctsf; apply: continuous_in_subspaceT => x Ix; apply: ctsf. by move: Ix; rewrite inE. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum finmap) mathcomp(matrix interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality) ereal reals signed topology prodnormedzmodule normedtype derive sequences real_interval HB(structures)