eq fusionne avec eqT et devient par défaut sur Type,

idem pour ex et exT, ex2 et exT2, all et allT


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@3812 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 40 insertions, 3 deletions

diff --git a/theories/Init/Logic_Type.v b/theories/Init/Logic_Type.v
index e4982c1f6..de4d2721f 100755
--- a/theories/Init/Logic_Type.v
+++ b/theories/Init/Logic_Type.v
@@ -18,7 +18,11 @@ Require LogicSyntax.
 (** [allT A P], or simply [(ALLT x | P(x))], stands for [(x:A)(P x)]
    when [A] is of type [Type] *)
 
+(*
 Definition allT := [A:Type][P:A->Prop](x:A)(P x). 
+*)
+
+Syntactic Definition allT := all.
 
 Section universal_quantification.
 
@@ -27,7 +31,7 @@ Variable P : A->Prop.
 
 Theorem inst :  (x:A)(allT ? [x](P x))->(P x).
 Proof.
-Unfold allT; Auto.
+Unfold all; Auto.
 Qed.
 
 Theorem gen : (B:Prop)(f:(y:A)B->(P y))B->(allT A P).
@@ -45,12 +49,23 @@ End universal_quantification.
 (** [exT2 A P Q], or simply [(EXT x | P(x) & Q(x))], stands for the
     existential quantification on both [P] and [Q] when [A] is of
     type [Type] *)
-
+(*
 Inductive  exT [A:Type;P:A->Prop] : Prop
     := exT_intro : (x:A)(P x)->(exT A P).
+*)
+
+Syntactic Definition exT := ex.
+Syntactic Definition exT_intro := ex_intro.
+Syntactic Definition exT_ind  := ex_ind.
 
+(*
 Inductive exT2 [A:Type;P,Q:A->Prop] : Prop
     := exT_intro2 : (x:A)(P x)->(Q x)->(exT2 A P Q).
+*)
+
+Syntactic Definition exT2 := ex2.
+Syntactic Definition exT_intro2 := ex_intro2.
+Syntactic Definition exT2_ind  := ex2_ind.
 
 (** Leibniz equality : [A:Type][x,y:A] (P:A->Prop)(P x)->(P y)
 
@@ -58,11 +73,20 @@ Inductive exT2 [A:Type;P,Q:A->Prop] : Prop
    type [Type]. This equality satisfies reflexivity (by definition), 
    symmetry, transitivity and stability by congruence *)
 
+
+(*
 Inductive eqT [A:Type;x:A] : A -> Prop
                        := refl_eqT : (eqT A x x).
 
-Hints Resolve refl_eqT exT_intro2 exT_intro : core v62.
+Hints Resolve refl_eqT (* exT_intro2 exT_intro *) : core v62.
+*)
+Syntactic Definition eqT      := eq.
+Syntactic Definition refl_eqT := refl_equal.
+Syntactic Definition eqT_ind  := eq_ind.
+Syntactic Definition eqT_rect := eq_rect.
+Syntactic Definition eqT_rec  := eq_rec.
 
+(*
 Section Equality_is_a_congruence.
 
  Variables A,B : Type.
@@ -91,11 +115,19 @@ Section Equality_is_a_congruence.
  Qed.
 
 End Equality_is_a_congruence.
+*)
+Syntactic Definition sym_eqT  := sym_eq.
+Syntactic Definition trans_eqT  := trans_eq.
+Syntactic Definition congr_eqT  := f_equal.
+Syntactic Definition sym_not_eqT  := sym_not_eq.
 
+(*
 Hints Immediate sym_eqT sym_not_eqT : core v62.
+*)
 
 (** This states the replacement of equals by equals *)
 
+(*
 Definition eqT_ind_r : (A:Type)(x:A)(P:A->Prop)(P x)->(y:A)(eqT ? y x)->(P y).
 Intros A x P H y H0; Case sym_eqT with 1:=H0; Trivial.
 Defined.
@@ -107,6 +139,11 @@ Defined.
 Definition eqT_rect_r : (A:Type)(x:A)(P:A->Type)(P x)->(y:A)(eqT ? y x)->(P y).
 Intros A x P H y H0; Case sym_eqT with 1:=H0; Trivial.
 Defined.
+*)
+
+Syntactic Definition eqT_ind_r  := eq_ind_r.
+Syntactic Definition eqT_rec_r  := eq_rec_r.
+Syntactic Definition eqT_rect_r  := eq_rect_r.
 
 (** Some datatypes at the [Type] level *)