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[helm.git] / matita / matita / contribs / lambda_delta / Ground_2 / tri.ma

diff --git a/matita/matita/contribs/lambda_delta/Ground_2/tri.ma b/matita/matita/contribs/lambda_delta/Ground_2/tri.ma
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--- a/matita/matita/contribs/lambda_delta/Ground_2/tri.ma
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "Ground_2/arith.ma".
-
-(* TRICOTOMY FUNCTION *******************************************************)
-
-let rec tri (A:Type[0]) m n a b c on m : A ≝
-  match m with 
-  [ O   ⇒ match n with [ O ⇒ b | S n ⇒ a ]
-  | S m ⇒ match n with [ O ⇒ c | S n ⇒ tri A m n a b c ]
-  ]. 
-
-(* Basic properties *********************************************************)
-
-lemma tri_lt: ∀A,a,b,c,n,m. m < n → tri A m n a b c = a.
-#A #a #b #c #n elim n -n
-[ #m #H elim (lt_zero_false … H)
-| #n #IH #m elim m -m // /3 width=1/
-]
-qed.
-
-lemma tri_eq: ∀A,a,b,c,m. tri A m m a b c = b.
-#A #a #b #c #m elim m -m normalize //
-qed.
-
-lemma tri_gt: ∀A,a,b,c,m,n. n < m → tri A m n a b c = c.
-#A #a #b #c #m elim m -m
-[ #n #H elim (lt_zero_false … H)
-| #m #IH #n elim n -n // /3 width=1/
-]
-qed.
-