#[local] Infix " \in " := E.In.
#[local] Infix " \subseteq " := E.isSubsetOf.
#[local] Notation In := List.In.
#[local] Hint Resolve E.insert_monotonic : core.
Proof with (simpl in *; tauto) || eauto with *.
ii. eapply ENTAILS1; done!.
Qed.

Theorem the_propositional_soundness_theorem (X : ensemble formula) (b : formula)
(INFERS : X ⊢ b)
: X ⊨ b.