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+Axiom checker_flags : Set.
+
+Inductive Box (R : Type) : Type := box : Box R.
+
+Inductive typing (H : checker_flags) : Type :=
+| type_Rel : typing H -> typing H
+| type_Case : let i := tt in Box (typing H) -> typing H.
+
+Definition unbox (P : Type) (b : Box P) := match b with box _ => 0 end.
+
+Definition size (H : checker_flags) (d : typing H) : nat.
+Proof.
+revert d.
+fix size 1.
+destruct 1.
+- exact (size d).
+- exact (unbox _ b).
+Defined.
+
+Definition foo (H : checker_flags) (a : typing H) :
+ size H (type_Rel H a) = size H a.
+Proof.
+simpl.
+reflexivity.
+Qed.
+
+Definition bar (H : checker_flags) (a : typing H) :
+ size H (type_Rel H a) = size H a.
+Proof.
+vm_compute.
+reflexivity.
+Qed.
+
+Definition qux (H : checker_flags) (a : typing H) :
+ size H (type_Rel H a) = size H a.
+Proof.
+native_compute.
+reflexivity.
+Qed.