proposition: Lemma tree_map_props : exists f : T -> X, [/\ continuous f, set_surj [set: T] [set: X] f & (forall n U, trivIset [set: K n] (@refine_apx n U)) -> set_inj [set: T] f].
proof: Proof. exists tree_map; split. - exact: tree_map_cts. - exact: tree_map_surj. - exact: tree_map_inj. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum interval rat) mathcomp(finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality) reals signed topology HB(structures)