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(*                                                                    *)
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(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	       Category Parallel Arrowd (used in Equalizers)		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export BasicTypes.
Require Export Category.
Set Implicit Arguments.
Unset Strict Implicit.
Section pa_def.
Variables (C : Category) (a b : C) (I : Type) (k : I -> (a --> b)).
Inductive PA_ob : Type :=
| PA1 : PA_ob
| PA2 : PA_ob.
Inductive PA_mor : PA_ob -> PA_ob -> Type :=
| PA_I1 : PA_mor PA1 PA1
| PA_I2 : PA_mor PA2 PA2
| PA_f : I -> PA_mor PA1 PA2.
(* sche'mas d'e'limination pour PA_mor *)

(* Specifications: *)
Lemma PA_11_P :
(PA_mor PA1 PA1 -> Prop) -> forall x y : PA_ob, PA_mor x y -> Prop.
Lemma PA_22_P :
(PA_mor PA2 PA2 -> Prop) -> forall x y : PA_ob, PA_mor x y -> Prop.
Lemma PA_12_P :
(PA_mor PA1 PA2 -> Prop) -> forall x y : PA_ob, PA_mor x y -> Prop.
Lemma PA_21_P :
(PA_mor PA2 PA1 -> Prop) -> forall x y : PA_ob, PA_mor x y -> Prop.
Lemma PA_21_T :
(PA_mor PA2 PA1 -> Type) -> forall x y : PA_ob, PA_mor x y -> Type.