X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Fcongruence.ma;h=948d10667261ddc7971811c359f65424a0741aef;hb=98c84d48f4511cb52c8dc03881e113bd4bd9c6ce;hp=af744cf3475087290d2100638f3a6af3b729c732;hpb=55b82bd235d82ff7f0a40d980effe1efde1f5073;p=helm.git

diff --git a/helm/software/matita/library/nat/congruence.ma b/helm/software/matita/library/nat/congruence.ma
index af744cf34..948d10667 100644
--- a/helm/software/matita/library/nat/congruence.ma
+++ b/helm/software/matita/library/nat/congruence.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/congruence".
-
 include "nat/relevant_equations.ma".
 include "nat/primes.ma".
 
@@ -23,6 +21,13 @@ 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 +94,18 @@ 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.
@@ -101,7 +118,7 @@ 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.
@@ -166,10 +183,9 @@ 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.