autobatch by

diff --git a/helm/software/matita/library/nat/gcd.ma b/helm/software/matita/library/nat/gcd.ma
index 395b24248f692366330c48ec002ed5c82bb095bd..aa512566e7cc6735bb8e409b94a97f298bfcdf75 100644 (file)
--- a/helm/software/matita/library/nat/gcd.ma
+++ b/helm/software/matita/library/nat/gcd.ma
@@ -755,11 +755,10 @@ cut (n \divides p \lor n \ndivides p)
     |right.
      cut (\exists a,b. a*n - b*p = (S O) \lor b*p - a*n = (S O))
        [elim Hcut1.elim H3.elim H4
-         [(* first case *)
-          rewrite > (times_n_SO q).rewrite < H5.
+         [rewrite > (times_n_SO q).rewrite < H5.
           rewrite > distr_times_minus.
-          elim H1. autobatch;
-          (*
+          elim H1. autobatch by witness, divides_minus.
+         (*
           rewrite > (sym_times q (a1*p)).
           rewrite > (assoc_times a1).
           applyS (witness n ? ? (refl_eq ? ?)).          
@@ -773,7 +772,7 @@ cut (n \divides p \lor n \ndivides p)
          |(* second case *)
           rewrite > (times_n_SO q).rewrite < H5.
           rewrite > distr_times_minus.
-          elim H1. autobatch;
+          elim H1. autobatch by witness, divides_minus.
           (*
           rewrite > (sym_times q (a1*p)).
           rewrite > (assoc_times a1).
@@ -878,19 +877,15 @@ cut (n \divides p \lor n \ndivides p)
     |cut (\exists a,b. a*n - b*m = (S O) \lor b*m - a*n = (S O))
       [elim Hcut1.elim H4.elim H5         
         [(* first case *)
+          elim H2. 
           rewrite > (times_n_SO p).rewrite < H6.
           rewrite > distr_times_minus.
-          rewrite > (sym_times p (a1*m)).
-          rewrite > (assoc_times a1).
-          elim H2.rewrite > H7. 
-          applyS (witness n ? ? (refl_eq ? ?)) (* timeout=50 *).
-         |(* second case *)
+          autobatch by witness, divides_minus.
+        |(* second case *)
+          elim H2.
           rewrite > (times_n_SO p).rewrite < H6.
           rewrite > distr_times_minus.
-          rewrite > (sym_times p (a1*m)).
-          rewrite > (assoc_times a1).
-          elim H2.rewrite > H7.
-          applyS (witness n ? ? (refl_eq ? ?)).
+          autobatch by witness, divides_minus.
         ](* end second case *)
      |rewrite < H1.apply eq_minus_gcd.
      ]
@@ -925,7 +920,8 @@ intros.elim H3.
 rewrite > H4 in H2.
 elim (divides_times_to_divides ? ? ? H H2)
   [apply False_ind.apply H1.assumption
-  |elim H5.  
+  |elim H5.
+   (* applyS (witness ? ? n2 (refl_eq ? ?)).*)
    apply (witness ? ? n2).
    rewrite > sym_times in ⊢ (? ? ? (? % ?)).
    rewrite > assoc_times.