- renamed ocaml/ to components/

[helm.git] / helm / matita / library / nat / relevant_equations.ma

diff --git a/helm/matita/library/nat/relevant_equations.ma b/helm/matita/library/nat/relevant_equations.ma
deleted file mode 100644 (file)
index f4cf437..0000000
--- a/helm/matita/library/nat/relevant_equations.ma
+++ /dev/null
@@ -1,50 +0,0 @@
-(**************************************************************************)
-(*       __                                                               *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
-(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU Lesser General Public License Version 2.1         *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/nat/relevant_equations.ma".
-
-include "nat/times.ma".
-include "nat/minus.ma".
-
-theorem times_plus_l: \forall n,m,p:nat. (n+m)*p = n*p + m*p.
-intros.
-apply (trans_eq ? ? (p*(n+m))).
-apply sym_times.
-apply (trans_eq ? ? (p*n+p*m)).
-apply distr_times_plus.
-apply eq_f2.
-apply sym_times.
-apply sym_times.
-qed.
-
-theorem times_minus_l: \forall n,m,p:nat. (n-m)*p = n*p - m*p.
-intros.
-apply (trans_eq ? ? (p*(n-m))).
-apply sym_times.
-apply (trans_eq ? ? (p*n-p*m)).
-apply distr_times_minus.
-apply eq_f2.
-apply sym_times.
-apply sym_times.
-qed.
-
-theorem times_plus_plus: \forall n,m,p,q:nat. (n + m)*(p + q) =
-n*p + n*q + m*p + m*q.
-intros.
-apply (trans_eq nat ? ((n*(p+q) + m*(p+q)))).
-apply times_plus_l.
-rewrite > distr_times_plus.
-rewrite > distr_times_plus.
-rewrite < assoc_plus.reflexivity.
-qed.