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+Require Import Program.
+
+Inductive Even : nat -> Prop :=
+| evenO : Even O
+| evenS : forall n, Odd n -> Even (S n)
+with Odd : nat -> Prop :=
+| oddS : forall n, Even n -> Odd (S n).
+Axiom admit : forall {T}, T.
+Program Fixpoint doubleE {n} (e : Even n) : Even (2 * n) := admit
+with doubleO {n} (o : Odd n) : Odd (S (2 * n)) := _.
+Next Obligation of doubleE.