X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FGround_2%2Ftri.ma;fp=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FGround_2%2Ftri.ma;h=0000000000000000000000000000000000000000;hb=eb918fc784eacd2094e3986ba321ef47690d9983;hp=005806c11c96e481e59a128aa877d05885db7d13;hpb=011cf6478141e69822a5b40933f2444d0522532f;p=helm.git diff --git a/matita/matita/contribs/lambda_delta/Ground_2/tri.ma b/matita/matita/contribs/lambda_delta/Ground_2/tri.ma deleted file mode 100644 index 005806c11..000000000 --- a/matita/matita/contribs/lambda_delta/Ground_2/tri.ma +++ /dev/null @@ -1,44 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||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. -