proposition: Lemma Urysohn_eq0 (A B : set T) : uniform_separator A B -> A !=set0 -> Urysohn A B @` A = [set 0].
proof: Proof. move=> eE Aa; have [_ _ /(_ eE)[As0 _]] := projT2 (cid (@Urysohn' A B)). rewrite eqEsubset; split => // ? ->; case: Aa => a ?; exists a => //. by apply: As0; exists a. 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