X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Flibrary%2Fnat%2Fcongruence.ma;h=f418c1b8578a0a7de9e983a96c7291fd28fc73c4;hb=8ee0e6f729105eaf1907de0baef22e170b0d17b3;hp=af744cf3475087290d2100638f3a6af3b729c732;hpb=7f2444c2670cadafddd8785b687ef312158376b0;p=helm.git

diff --git a/matita/library/nat/congruence.ma b/matita/library/nat/congruence.ma
index af744cf34..f418c1b85 100644
--- a/matita/library/nat/congruence.ma
+++ b/matita/library/nat/congruence.ma
@@ -23,6 +23,13 @@ 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 }.
+
 theorem congruent_n_n: \forall n,p:nat.congruent n n p.
 intros.unfold congruent.reflexivity.
 qed.
@@ -89,6 +96,18 @@ apply (div_mod_spec_to_eq2 n p (div n p) (mod n p) (r +(div m p)) (mod m p)).
 apply div_mod_spec_div_mod.assumption.
 constructor 1.
 apply lt_mod_m_m.assumption.
+(*cut (n = r * p + (m / p * p + m \mod p)).*)
+(*lapply (div_mod m p H). 
+rewrite > sym_times.
+rewrite > distr_times_plus.
+(*rewrite > (sym_times p (m/p)).*)
+(*rewrite > sym_times.*)
+rewrite > assoc_plus.
+autobatch paramodulation.
+rewrite < div_mod.
+assumption.
+assumption.
+*)
 rewrite > sym_times.
 rewrite > distr_times_plus.
 rewrite > sym_times.
@@ -166,10 +185,9 @@ qed.
 theorem congruent_pi: \forall f:nat \to nat. \forall n,m,p:nat.O < p \to
 congruent (pi n f m) (pi n (\lambda m. mod (f m) p) m) p.
 intros.
-elim n.change with (congruent (f m) (f m \mod p) p).
+elim n. simplify.
 apply congruent_n_mod_n.assumption.
-change with (congruent ((f (S n1+m))*(pi n1 f m)) 
-(((f (S n1+m))\mod p)*(pi n1 (\lambda m.(f m) \mod p) m)) p).
+simplify.
 apply congruent_times.
 assumption.
 apply congruent_n_mod_n.assumption.