blob: d7b3d036292fc761800294d94d810151a550ac03 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
|
(* *********************************************************************)
(* *)
(* The Compcert verified compiler *)
(* *)
(* Xavier Leroy, INRIA Paris-Rocquencourt *)
(* *)
(* Copyright Institut National de Recherche en Informatique et en *)
(* Automatique. All rights reserved. This file is distributed *)
(* under the terms of the GNU Lesser General Public License as *)
(* published by the Free Software Foundation, either version 2.1 of *)
(* the License, or (at your option) any later version. *)
(* This file is also distributed under the terms of the *)
(* INRIA Non-Commercial License Agreement. *)
(* *)
(* *********************************************************************)
(** This file collects some axioms used throughout the CompCert development. *)
Require ClassicalFacts.
Require FunctionalExtensionality.
(** * Extensionality axioms *)
(** The [Require FunctionalExtensionality] gives us functional
extensionality for dependent function types: *)
Lemma functional_extensionality_dep:
forall {A: Type} {B : A -> Type} (f g : forall x : A, B x),
(forall x, f x = g x) -> f = g.
Proof @FunctionalExtensionality.functional_extensionality_dep.
(** and, as a corollary, functional extensionality for non-dependent functions:
*)
Lemma functional_extensionality:
forall {A B: Type} (f g : A -> B), (forall x, f x = g x) -> f = g.
Proof @FunctionalExtensionality.functional_extensionality.
(** For compatibility with earlier developments, [extensionality]
is an alias for [functional_extensionality]. *)
Lemma extensionality:
forall {A B: Type} (f g : A -> B), (forall x, f x = g x) -> f = g.
Proof @functional_extensionality.
(** * Proof irrelevance *)
(** We also use proof irrelevance. *)
Axiom proof_irr: ClassicalFacts.proof_irrelevance.
Arguments proof_irr [A].
|
