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-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
-
-(* $Id$: *)
-
-Declare ML Module "setoid_replace".
-
-Grammar tactic simple_tactic : ast :=
- setoid_replace [ "Setoid_replace" constrarg($c1) "with" constrarg($c2) ] -> [(Setoid_replace $c1 $c2)]
-.
-
-Grammar tactic simple_tactic : ast :=
- setoid_rewriteLR [ "Setoid_rewrite" "->" constrarg($c) ] -> [(Setoid_rewriteLR $c)]
-| setoid_rewriteRL [ "Setoid_rewrite" "<-" constrarg($c) ] -> [(Setoid_rewriteRL $c)]
-| setoid_rewrite [ "Setoid_rewrite" constrarg($c) ] -> [(Setoid_rewriteLR $c)]
-.
-
-Syntax tactic level 0 :
- setoid_replace [<<(Setoid_replace $c1 $c2)>>] -> [[<hov 0>"Setoid_replace " $c1 [1 1] "with " $c2]]
- | setoid_rewritelr [<<(Setoid_rewriteLR $c)>>] -> ["Setoid_rewrite " $c]
- | setoid_rewriterl [<<(Setoid_rewriteRL $c)>>] -> ["Setoid_rewrite <- " $c]
-.
-
-Grammar vernac vernac : ast :=
- add_setoid [ "Add" "Setoid" constrarg($a) constrarg($aeq) constrarg($t) "." ]
- -> [(AddSetoid $a $aeq $t)]
-| new_morphism [ "New" "Morphism" identarg($s) constrarg($m) "." ] -> [(NamedNewMorphism $s $m)]
-| new_morphism [ "New" "Morphism" identarg($m) "." ] -> [(NewMorphism $m)]
-.
-
-Section Setoid.
-
-Variable A : Type.
-Variable Aeq : A -> A -> Prop.
-
-Record Setoid_Theory : Prop :=
-{ Seq_refl : (x:A) (Aeq x x);
- Seq_sym : (x,y:A) (Aeq x y) -> (Aeq y x);
- Seq_trans : (x,y,z:A) (Aeq x y) -> (Aeq y z) -> (Aeq x z)
-}.
-
-End Setoid.
-
-Definition Prop_S : (Setoid_Theory Prop ([x,y:Prop] x<->y)).
-Split; Tauto.
-Save.
-
-Add Setoid Prop iff Prop_S.
-
-Hint prop_set : setoid := Resolve (Seq_refl Prop iff Prop_S).
-Hint prop_set : setoid := Resolve (Seq_sym Prop iff Prop_S).
-Hint prop_set : setoid := Resolve (Seq_trans Prop iff Prop_S).
-
-New Morphism or.
-Tauto.
-Save.
-
-New Morphism and.
-Tauto.
-Save.
-
-New Morphism not.
-Tauto.
-Save.
-
-Definition fleche [A,B:Prop] := A -> B.
-
-New Morphism fleche.
-Tauto.
-Save.
-