proposition: Lemma lattice_finite_sup_aux f: Hf f -> nonempty (range f) /\ finite_set (range f).
proof: Proof. move=> [fgf fsd ned srf]; split; last by apply: finite_range. by move: ned => [x xd]; exists (Vg f x); fprops. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)