proposition: Lemma proper_image (T U : Type) (f : T -> U) (F : set_system T) : ProperFilter F -> f @` setT = setT -> ProperFilter [set f @` A | A in F].
proof: Proof. move=> FF fsurj; apply: Build_ProperFilter; last exact: filter_image. by move=> _ [A FA <-]; have /filter_ex [p Ap] := FA; exists (f p); exists p. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed