Module FolNotations.
Infix "≡" := alpha_equiv : type_scope.
Infix "⊨" := entails : type_scope.
Notation "Gamma ⊭ C" := (~ Gamma ⊨ C) : type_scope.
End FolNotations.
#[global]
Add Parametric Morphism {L : language}
: (@entails L) with signature (eqProp ==> alpha_equiv ==> iff)
as entails_compatWith_eqProp.

Lemma extend_entails {L : language} (Gamma : ensemble (@frm L)) (Gamma' : ensemble (@frm L)) (C : frm L)
(ENTAILS : Gamma ⊨ C)
(SUBSET : Gamma \subseteq Gamma')
: Gamma' ⊨ C.