ArrowDed.v

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(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)



(****************************************************************************)
(*                          Signes Project                                  *)
(*                            2002-2003                                     *)
(*                           Houda ANOUN                                    *)
(*                          Pierre Casteran                                 *)
(*                           LaBRI/INRIA                                    *)
(****************************************************************************)


Require Export GentzenDed.
Require Export ArrowGentzen.

Set Implicit Arguments.



Definition natDedToArrow :
  forall (Atoms:Set)(Gamma : Term Atoms) (F : Form Atoms) 
 (E : gentzen_extension)(X : arrow_extension),
  gentzenToArrowExt Atoms E X ->
  natDed E Gamma F -> arrow X (deltaTranslation Gamma) F.

 intros.
 eapply gentzenToArrow.
 eauto.
 apply natDedToGentzen.
 assumption.
Defined.


Definition arrowToNatDed :
  forall (Atoms:Set)(A B : Form Atoms) (E : gentzen_extension) (X : arrow_extension),
  condCutExt E ->
  arrowToGentzenExt Atoms X E ->
  arrow X A B -> natDed E (OneForm A) B.
 intros.
 apply gentzenToNatDed.
 auto.
 eapply arrowToGentzen.
 eauto.
 assumption.
Defined.