Set Implicit Arguments.
Unset Strict Implicit.

Module Type SIG.
  Parameter id : forall A : Set, A -> A.
End SIG.

Module M (X: SIG).
  Definition idid := X.id X.id.
  Definition id := idid X.id.
End M.

Module N := M.

Module Nat.
  Definition T := nat.
  Definition x := 0.
  Definition id (A : Set) (x : A) := x.
End Nat.

Module Z := N Nat.

Check (Z.idid 0).

Module P (Y: SIG) := N.

Module Y := P Nat Z.

Check (Y.id 0).