#[local] Infix " \in " := E.In.
#[local] Infix " \subseteq " := E.isSubsetOf.
#[local] Notation In := List.In.
#[local] Hint Resolve E.insert_monotonic : core.

Lemma ByAssumption_preserves (Gamma : ensemble formula) (C : formula)
(ELEM : C \in Gamma)
: Gamma ⊨ C.