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(* This requires cumulativity *)
Definition Type2 := Type.
Definition Type1 : Type2 := Type.
Lemma lem1 : (True -> Type1) -> Type2.
intro H.
apply H.
exact I.
Qed.
Lemma lem2 :
forall (A : Type) (P : A -> Type) (x : A),
(forall y : A, x = y -> P y) -> P x.
auto.
Qed.
Lemma lem3 : forall P : Prop, P.
intro P; pattern P in |- *.
apply lem2.
Abort.
(* Check managing of universe constraints in inversion *)
(* Bug report #855 *)
Inductive dep_eq : forall X : Type, X -> X -> Prop :=
| intro_eq : forall (X : Type) (f : X), dep_eq X f f
| intro_feq :
forall (A : Type) (B : A -> Type),
let T := forall x : A, B x in
forall (f g : T) (x : A), dep_eq (B x) (f x) (g x) -> dep_eq T f g.
Require Import Relations.
Theorem dep_eq_trans : forall X : Type, transitive X (dep_eq X).
Proof.
unfold transitive in |- *.
intros X f g h H1 H2.
inversion H1.
Abort.
(* Submitted by Bas Spitters (bug report #935) *)
(* This is a problem with the status of the type in LetIn: is it a
user-provided one or an inferred one? At the current time, the
kernel type-check the type in LetIn, which means that it must be
considered as user-provided when calling the kernel. However, in
practice it is inferred so that a universe refresh is needed to set
its status as "user-provided".
Especially, universe refreshing was not done for "set/pose" *)
Lemma ind_unsec : forall Q : nat -> Type, True.
intro.
set (C := forall m, Q m -> Q m).
exact I.
Qed.
|
