proposition: Lemma Exercise4_7j a: inc a (substrate r) -> gle r (supremum r (E47S r a)) a.
proof: Proof. move => asr; move: (Exercise4_7h asr) => ne. have sE: sub (E47S r a) (substrate r) by apply: Zo_S. apply /(lattice_finite_sup3P lr _ (sub_finite_set sE fs) ne sE). by move=> z /Zo_hi []. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)