Section Typing.
Variable (E: list deq).
Hint Resolve Vars__de_in : core.
Definition Gamma__dwk := repeat (alpha → (alpha → alpha) → alpha) (S (Sum (Vars__de E))).
Hint Resolve Gamma__dwk_nth : core.

Lemma typing_addEQ x y z:
x +ₑ y =ₑ z ∈ E -> Gamma__dwk ⊢₂(3) addEQ x y z : alpha → (alpha → alpha) → alpha.