proposition: Lemma set_meet_le_incl S S' : S `<=` S' -> set_meet S' <= set_meet S.
proof: Proof. move=> SS'; apply: set_meet_ge_lb => x Sx; exact/set_meet_lb/SS'. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype choice order) mathcomp(ssrnat bigop classical_sets)