Instance forAllMonotonic {A C} {_ : Checkable C} `{Show A} (g : G A) (f : A -> C)
`{SizeMonotonic _ g} `{forall x, SizeMonotonicChecker (checker (f x))} :
SizeMonotonicChecker (forAll g f).
Admitted.

(* begin semForAllSizeMonotonic *)
Lemma semForAllSizeMonotonic {A C} `{Show A, Checkable C} (g : G A) (f : A -> C)
`{SizeMonotonic _ g} `{forall a, SizeMonotonicChecker (checker (f a))} :
(semChecker (forAll g f) <-> forall (a:A), a \in semGen g -> semCheckable (f a)).