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Require Import Program.
Axiom I : Type.
Inductive S : Type := NT : I -> S.
Axiom F : S -> Type.
Axiom G : forall (s : S), F s -> Type.
Section S.
Variable init : I.
Variable my_s : F (NT init).
Inductive foo : forall (s: S) (hole_sem: F s), Type :=
| Foo : foo (NT init) my_s.
Goal forall
(n : I) (s : F (NT n)) (ptz : foo (NT n) s) (pt : G (NT n) s) (x : unit),
match
match x with tt => tt end
with
| tt =>
match
match ptz in foo x s return (forall _ : G x s, unit) with
| Foo => fun _ : G (NT init) my_s => tt
end pt
with
| tt => False
end
end.
Proof.
dependent destruction ptz.
(* Check well-typedness of goal *)
match goal with [ |- ?P ] => let t := type of P in idtac end.
Abort.
End S.
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