proposition: Lemma normal_openP : normal_space T <-> forall (A B : set T), closed A -> closed B -> A `&` B = set0 -> exists U V, [/\ open U, open V, A `<=` U, B `<=` V & U `&` V = set0].
proof: Proof. exact: (normal_spaceP 0%N 2%N). Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule