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+Structure Inner := mkI { is :> Type }.
+Structure Outer := mkO { os :> Inner }.
+
+Canonical Structure natInner := mkI nat.
+Canonical Structure natOuter := mkO natInner.
+
+Definition hidden_nat := nat.
+
+Axiom P : forall S : Outer, is (os S) -> Prop.
+
+Lemma foo (n : hidden_nat) : P _ n.
+Admitted.