Definition eq_dec (E : Set) := forall a b : E, {a = b} + {a <> b}.

Lemma case_ineq : forall (E F : Set) (eq_E_dec : eq_dec E) (x x' : E) (y z : F), x <> x' -> match eq_E_dec x x' with | left _ => y | right _ => z end = z.