Section PACO.
#[local] Hint Resolve le_join_lattice_introl le_join_lattice_intror join_lattice_le_intro bot_lattice_le_intro : core.
Context {A : Type}.

Lemma union_join_lattice_spec (X1 : ensemble A) (X2 : ensemble A)
: is_supremum_of (@E.union A X1 X2) (E.fromList [X1; X2]).