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+(*Suppose we have*)
+
+  Inductive my_if {A B} : bool -> Type :=
+  | then_case (_ : A) : my_if true
+  | else_case (_ : B) : my_if false.
+  Notation "'If' b 'Then' A 'Else' B" := (@my_if A B b) (at level 10).
+
+(*then here are three inductive type declarations that work:*)
+
+  Inductive I1 :=
+  | i1 (x : I1).
+  Inductive I2 :=
+  | i2 (x : nat).
+  Inductive I3 :=
+  | i3 (b : bool) (x : If b Then I3 Else nat).
+
+(*and here is one that does not, despite being equivalent to [I3]:*)
+
+  Fail Inductive I4 :=
+  | i4 (b : bool) (x : if b then I4 else nat). (* Error: Non strictly positive occurrence of "I4" in
+   "forall b : bool, (if b then I4 else nat) -> I4". *)
+
+(*I think this one should work.  I believe this is a conservative extension over CIC: Since [match] statements returning types can always be re-encoded as inductive type families, the analysis should be independent of whether the constructor uses an inductive or a [match] statement.*)