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Set Universe Polymorphism.
Set Polymorphic Inductive Cumulativity.
Set Printing Universes.
Inductive List (A: Type) := nil | cons : A -> List A -> List A.
Section ListLift.
Universe i j.
Constraint i < j.
Definition LiftL {A} : List@{i} A -> List@{j} A := fun x => x.
End ListLift.
Lemma LiftL_Lem A (l : List A) : l = LiftL l.
Proof. reflexivity. Qed.
Section ListLower.
Universe i j.
Constraint i < j.
Definition LowerL {A : Type@{i}} : List@{j} A -> List@{i} A := fun x => x.
End ListLower.
Lemma LowerL_Lem@{i j|j<i+} (A : Type@{j}) (l : List@{i} A) : l = LowerL@{j i} l.
Proof. reflexivity. Qed.
(*
I disable these tests because cqochk can't process them when compiled with
ocaml-4.02.3+32bit and camlp5-4.16 which is the case for Travis!
I have added this file (including the commented parts below) in
test-suite/success/cumulativity.v which doesn't run coqchk on them.
*)
(* Inductive Tp := tp : Type -> Tp. *)
(* Section TpLift. *)
(* Universe i j. *)
(* Constraint i < j. *)
(* Definition LiftTp : Tp@{i} -> Tp@{j} := fun x => x. *)
(* End TpLift. *)
(* Lemma LiftC_Lem (t : Tp) : LiftTp t = t. *)
(* Proof. reflexivity. Qed. *)
(* Section TpLower. *)
(* Universe i j. *)
(* Constraint i < j. *)
(* Fail Definition LowerTp : Tp@{j} -> Tp@{i} := fun x => x. *)
(* End TpLower. *)
(* Section subtyping_test. *)
(* Universe i j. *)
(* Constraint i < j. *)
(* Inductive TP2 := tp2 : Type@{i} -> Type@{j} -> TP2. *)
(* End subtyping_test. *)
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