diff options
Diffstat (limited to 'theories/Logic/EqdepFacts.v')
| -rw-r--r-- | theories/Logic/EqdepFacts.v | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/theories/Logic/EqdepFacts.v b/theories/Logic/EqdepFacts.v index d84cd824..a22f286e 100644 --- a/theories/Logic/EqdepFacts.v +++ b/theories/Logic/EqdepFacts.v @@ -1,7 +1,7 @@ (* -*- coding: utf-8 -*- *) (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -101,7 +101,7 @@ Section Dependent_Equality. forall (p q:U) (x:P p) (y:P q), eq_dep p x q y -> eq_dep1 p x q y. Proof. destruct 1. - apply eq_dep1_intro with (refl_equal p). + apply eq_dep1_intro with (eq_refl p). simpl; trivial. Qed. @@ -121,7 +121,7 @@ Proof. apply eq_dep_intro. Qed. -Notation eq_sigS_eq_dep := eq_sigT_eq_dep (only parsing). (* Compatibility *) +Notation eq_sigS_eq_dep := eq_sigT_eq_dep (compat "8.2"). (* Compatibility *) Lemma eq_dep_eq_sigT : forall (U:Type) (P:U -> Type) (p q:U) (x:P p) (y:P q), @@ -250,12 +250,12 @@ Section Equivalences. (** Uniqueness of Reflexive Identity Proofs *) Definition UIP_refl_ := - forall (x:U) (p:x = x), p = refl_equal x. + forall (x:U) (p:x = x), p = eq_refl x. (** Streicher's axiom K *) Definition Streicher_K_ := - forall (x:U) (P:x = x -> Prop), P (refl_equal x) -> forall p:x = x, P p. + forall (x:U) (P:x = x -> Prop), P (eq_refl x) -> forall p:x = x, P p. (** Injectivity of Dependent Equality is a consequence of *) (** Invariance by Substitution of Reflexive Equality Proof *) @@ -389,14 +389,14 @@ Proof (eq_dep_eq__UIP U eq_dep_eq). (** Uniqueness of Reflexive Identity Proofs is a direct instance of UIP *) -Lemma UIP_refl : forall (x:U) (p:x = x), p = refl_equal x. +Lemma UIP_refl : forall (x:U) (p:x = x), p = eq_refl x. Proof (UIP__UIP_refl U UIP). (** Streicher's axiom K is a direct consequence of Uniqueness of Reflexive Identity Proofs *) Lemma Streicher_K : - forall (x:U) (P:x = x -> Prop), P (refl_equal x) -> forall p:x = x, P p. + forall (x:U) (P:x = x -> Prop), P (eq_refl x) -> forall p:x = x, P p. Proof (UIP_refl__Streicher_K U UIP_refl). End Axioms. |