proposition: Lemma image_smaller f: function f -> (Imf f) <=cc (source f).
proof: Proof. move=> ff. apply: surjective_cle. exists (restriction_to_image f). split; rewrite/ restriction_to_image /restriction2; aw; trivial. exact: (restriction_to_image_fs ff). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)