update in groud_2 and models

[helm.git] / helm / software / matita / library / nat / congruence.ma

diff --git a/helm/software/matita/library/nat/congruence.ma b/helm/software/matita/library/nat/congruence.ma
index f418c1b8578a0a7de9e983a96c7291fd28fc73c4..0a635ff78d9dc98ce0e68bae63b028a218ef7b64 100644 (file)
--- a/helm/software/matita/library/nat/congruence.ma
+++ b/helm/software/matita/library/nat/congruence.ma
@@ -1,5 +1,5 @@
 (**************************************************************************)
-(*       ___                                                             *)
+(*       ___                                                               *)
 (*      ||M||                                                             *)
 (*      ||A||       A project by Andrea Asperti                           *)
 (*      ||T||                                                             *)
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/congruence".
-
 include "nat/relevant_equations.ma".
 include "nat/primes.ma".
 
@@ -23,12 +21,7 @@ definition S_mod: nat \to nat \to nat \def
 definition congruent: nat \to nat \to nat \to Prop \def
 \lambda n,m,p:nat. mod n p = mod m p.
 
-interpretation "congruent" 'congruent n m p =
-  (cic:/matita/nat/congruence/congruent.con n m p).
-
-notation < "hvbox(n break \cong\sub p m)"
-  (*non associative*) with precedence 45
-for @{ 'congruent $n $m $p }.
+interpretation "congruent" 'congruent n m p = (congruent n m p).
 
 theorem congruent_n_n: \forall n,p:nat.congruent n n p.
 intros.unfold congruent.reflexivity.
@@ -120,7 +113,7 @@ qed.
 theorem divides_to_congruent: \forall n,m,p:nat. O < p \to m \le n \to 
 divides p (n - m) \to congruent n m p.
 intros.elim H2.
-apply (eq_times_plus_to_congruent n m p n2).
+apply (eq_times_plus_to_congruent n m p n1).
 assumption.
 rewrite < sym_plus.
 apply minus_to_plus.assumption.