X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Ffactorization.ma;h=0bd8e247836bb10a679b9f648f0603a1a5a899dc;hb=db9c252cc8adb9243892203805b203bafe486bfc;hp=4c8de0f51ff3e112205dda4c97d26ae1b9939bca;hpb=58c80e82b2e0aea89e18e588028fb0f53479c219;p=helm.git

diff --git a/helm/software/matita/library/nat/factorization.ma b/helm/software/matita/library/nat/factorization.ma
index 4c8de0f51..0bd8e2478 100644
--- a/helm/software/matita/library/nat/factorization.ma
+++ b/helm/software/matita/library/nat/factorization.ma
@@ -27,10 +27,10 @@ definition max_prime_factor \def \lambda n:nat.
 theorem divides_max_prime_factor_n:
   \forall n:nat. (S O) < n
   \to nth_prime (max_prime_factor n) \divides n.
-intros; apply divides_b_true_to_divides;
-[ apply lt_O_nth_prime_n;
-| apply (f_max_true  (\lambda p:nat.eqb (n \mod (nth_prime p)) O) n);
-  cut (\exists i. nth_prime i = smallest_factor n);
+intros.
+apply divides_b_true_to_divides.
+apply (f_max_true  (\lambda p:nat.eqb (n \mod (nth_prime p)) O) n);
+cut (\exists i. nth_prime i = smallest_factor n);
   [ elim Hcut.
     apply (ex_intro nat ? a);
     split;
@@ -46,17 +46,17 @@ intros; apply divides_b_true_to_divides;
       [ apply (trans_lt ? (S O));
         [ unfold lt; apply le_n;
         | apply lt_SO_smallest_factor; assumption; ]
-      | letin x \def le.auto.
+      | letin x \def le.autobatch new.
          (*       
        apply divides_smallest_factor_n;
         apply (trans_lt ? (S O));
         [ unfold lt; apply le_n;
         | assumption; ] *) ] ]
-  | letin x \def prime. auto.
+  | autobatch. 
     (* 
     apply prime_to_nth_prime;
     apply prime_smallest_factor_n;
-    assumption; *) ] ]
+    assumption; *) ] 
 qed.
 
 theorem divides_to_max_prime_factor : \forall n,m. (S O) < n \to O < m \to n \divides m \to 
@@ -70,8 +70,8 @@ apply divides_to_divides_b_true.
 cut (prime (nth_prime (max_prime_factor n))).
 apply lt_O_nth_prime_n.apply prime_nth_prime.
 cut (nth_prime (max_prime_factor n) \divides n).
-auto.
-auto.
+autobatch.
+autobatch.
 (*
   [ apply (transitive_divides ? n);
     [ apply divides_max_prime_factor_n.
@@ -90,6 +90,17 @@ auto.
 *)  
 qed.
 
+theorem divides_to_max_prime_factor1 : \forall n,m. O < n \to O < m \to n \divides m \to 
+max_prime_factor n \le max_prime_factor m.
+intros 3.
+elim (le_to_or_lt_eq ? ? H)
+  [apply divides_to_max_prime_factor
+    [assumption|assumption|assumption]
+  |rewrite < H1.
+   simplify.apply le_O_n.
+  ]
+qed.
+
 theorem p_ord_to_lt_max_prime_factor: \forall n,p,q,r. O < n \to
 p = max_prime_factor n \to 
 (pair nat nat q r) = p_ord n (nth_prime p) \to
@@ -105,7 +116,7 @@ apply divides_max_prime_factor_n.
 assumption.unfold Not.
 intro.
 cut (r \mod (nth_prime (max_prime_factor n)) \neq O);
-  [unfold Not in Hcut1.auto.
+  [unfold Not in Hcut1.autobatch new.
     (*
     apply Hcut1.apply divides_to_mod_O;
     [ apply lt_O_nth_prime_n.
@@ -114,7 +125,7 @@ cut (r \mod (nth_prime (max_prime_factor n)) \neq O);
     *)
   |letin z \def le.
    cut(pair nat nat q r=p_ord_aux n n (nth_prime (max_prime_factor n)));
-   [2: rewrite < H1.assumption.|letin x \def le.auto width = 4]
+   [2: rewrite < H1.assumption.|letin x \def le.autobatch width = 4 depth = 2]
    (* CERCA COME MAI le_n non lo applica se lo trova come Const e non Rel *)
   ].
 (*
@@ -126,20 +137,13 @@ cut (r \mod (nth_prime (max_prime_factor n)) \neq O);
     ]
   ].
 *)  
-cut (n=r*(nth_prime p)\sup(q));
-  [letin www \def le.letin www1 \def divides.
-   auto.
-(*
 apply (le_to_or_lt_eq (max_prime_factor r)  (max_prime_factor n)).
 apply divides_to_max_prime_factor.
 assumption.assumption.
 apply (witness r n ((nth_prime p) \sup q)).
-*)
- |
 rewrite < sym_times.
 apply (p_ord_aux_to_exp n n ? q r).
 apply lt_O_nth_prime_n.assumption.
-]
 qed.
 
 theorem p_ord_to_lt_max_prime_factor1: \forall n,p,q,r. O < n \to
@@ -395,7 +399,6 @@ apply (not_eq_O_S (S m1)).
 rewrite > Hcut.rewrite < H1.rewrite < times_n_O.reflexivity.
 apply le_to_or_lt_eq.apply le_O_n.
 (* prova del cut *)
-goal 20.
 apply (p_ord_aux_to_exp (S(S m1))).
 apply lt_O_nth_prime_n.
 assumption.