X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Flibrary%2Fnat%2Ffactorization.ma;h=d0036e4a1fcc147add9d888f359ee80c090ccb09;hb=061e94c62f89915a193ebd342cefe4be1f8d2869;hp=4c8de0f51ff3e112205dda4c97d26ae1b9939bca;hpb=c0b3eeafbeea89d16f0615d07ddfe38f2ce10219;p=helm.git

diff --git a/matita/library/nat/factorization.ma b/matita/library/nat/factorization.ma
index 4c8de0f51..d0036e4a1 100644
--- a/matita/library/nat/factorization.ma
+++ b/matita/library/nat/factorization.ma
@@ -46,13 +46,13 @@ 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.auto new.
          (*       
        apply divides_smallest_factor_n;
         apply (trans_lt ? (S O));
         [ unfold lt; apply le_n;
         | assumption; ] *) ] ]
-  | letin x \def prime. auto.
+  | letin x \def prime. auto new.
     (* 
     apply prime_to_nth_prime;
     apply prime_smallest_factor_n;
@@ -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.
+auto new.
+auto new.
 (*
   [ apply (transitive_divides ? n);
     [ apply divides_max_prime_factor_n.
@@ -105,7 +105,7 @@ 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.auto new.
     (*
     apply Hcut1.apply divides_to_mod_O;
     [ apply lt_O_nth_prime_n.
@@ -114,7 +114,7 @@ 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.auto width = 4 new]
    (* CERCA COME MAI le_n non lo applica se lo trova come Const e non Rel *)
   ].
 (*
@@ -126,20 +126,13 @@ 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