ExampleNatDed3.v

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

Require Import Tactics.

(* Derivation of the relative sentence 'that Peter wrote' in the 
system L using natural deduction rules of inference *)


Inductive Atoms : Set :=
  | np : Atoms
  | s : Atoms
  | r : Atoms.

Definition relativeSentence :
  natDed L_Sequent
    (Comma (OneForm (Slash (At r) (Slash (At s) (At np))))
       (Comma (OneForm (At np))
          (OneForm (Slash (Backslash (At np) (At s)) (At np))))) (
    At r).
 eapply SlashElim.
 constructor 1.
 apply SlashIntro.
 lNaturalTac (nil (A:=path)) LR.
 eapply BackSlashElim.
 constructor 1.
 eapply SlashElim; constructor 1.
Defined.