proposition: Lemma Urysohn_eq1 (A B : set T) : uniform_separator A B -> (B !=set0) -> (Urysohn A B) @` B = [set 1].
proof: Proof. move=> eE Bb; have [_ _ /(_ eE)[_ Bs0]] := projT2 (cid (@Urysohn' A B)). rewrite eqEsubset; split => // ? ->; case: Bb => b ?; exists b => //. by apply: Bs0; exists b. 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