Old tiny freescale experiment get rid of.

[helm.git] / helm / software / matita / library / assembly / extra.ma

diff --git a/helm/software/matita/library/assembly/extra.ma b/helm/software/matita/library/assembly/extra.ma
deleted file mode 100644 (file)
index be15c75..0000000
--- a/helm/software/matita/library/assembly/extra.ma
+++ /dev/null
@@ -1,84 +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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/assembly/extra".
-
-include "nat/div_and_mod.ma".
-include "nat/primes.ma".
-include "list/list.ma".
-
-axiom mod_plus: ∀a,b,m. (a + b) \mod m = (a \mod m + b \mod m) \mod m.
-axiom mod_mod: ∀a,n,m. n∣m → a \mod n = a \mod n \mod m.
-axiom eq_mod_times_n_m_m_O: ∀n,m. O < m → n * m \mod m = O.
-axiom eq_mod_to_eq_plus_mod: ∀a,b,c,m. a \mod m = b \mod m → (a+c) \mod m = (b+c) \mod m.
-axiom eq_mod_times_times_mod: ∀a,b,n,m. m = a*n → (a*b) \mod m = a * (b \mod n).
-axiom divides_to_eq_mod_mod_mod: ∀a,n,m. n∣m → a \mod m \mod n = a \mod n.
-axiom le_to_le_plus_to_le : ∀a,b,c,d.b\leq d\rarr a+b\leq c+d\rarr a\leq c.
-axiom or_lt_le : ∀n,m. n < m ∨ m ≤ n.
-
-inductive cartesian_product (A,B: Type) : Type ≝
- couple: ∀a:A.∀b:B. cartesian_product A B.
-
-lemma le_to_lt: ∀n,m. n ≤ m → n < S m.
- intros;
- autobatch.
-qed.
-
-alias num (instance 0) = "natural number".
-definition nat_of_bool ≝
- λb. match b with [ true ⇒ 1 | false ⇒ 0 ].
-
-theorem lt_trans: ∀x,y,z. x < y → y < z → x < z.
- unfold lt;
- intros;
- autobatch.
-qed.
-
-lemma leq_m_n_to_eq_div_n_m_S: ∀n,m:nat. 0 < m → m ≤ n → ∃z. n/m = S z.
- intros;
- unfold div;
- apply (ex_intro ? ? (div_aux (pred n) (n-m) (pred m)));
- cut (∃w.m = S w);
-  [ elim Hcut;
-    rewrite > H2;
-    rewrite > H2 in H1;
-    clear Hcut; clear H2; clear H; (*clear m;*)
-    simplify;
-    unfold in ⊢ (? ? % ?);
-    cut (∃z.n = S z);
-     [ elim Hcut; clear Hcut;
-       rewrite > H in H1;
-       rewrite > H; clear m;
-       change in ⊢ (? ? % ?)  with
-        (match leb (S a1) a with
-         [ true ⇒ O
-         | false ⇒ S (div_aux a1 ((S a1) - S a) a)]);
-       cut (S a1 ≰ a);
-        [ apply (leb_elim (S a1) a);
-           [ intro;
-             elim (Hcut H2)
-           | intro;
-             simplify;
-             reflexivity
-           ]
-        | intro;
-          autobatch
-        ]
-     | elim H1; autobatch
-     ]
-  | autobatch
-  ].
-qed.
-
-axiom daemon: False.