some corrections ...

[helm.git] / helm / software / matita / library / nat / generic_iter_p.ma

diff --git a/helm/software/matita/library/nat/generic_iter_p.ma b/helm/software/matita/library/nat/generic_iter_p.ma
index 4796ec10b2e14c1829daefba403a11b34e98e38d..7f51ac700c18e1a391e96c03c7462d1db03c536f 100644 (file)
--- a/helm/software/matita/library/nat/generic_iter_p.ma
+++ b/helm/software/matita/library/nat/generic_iter_p.ma
@@ -158,8 +158,7 @@ iter_p_gen (k + n) p A g baseA plusA
 intros.
 
 elim k
-[ rewrite < (plus_n_O n).
-  simplify.
+[ simplify.
   rewrite > H in \vdash (? ? ? %).
   rewrite > (H1 ?).
   reflexivity
@@ -283,8 +282,7 @@ elim n
           rewrite > sym_plus.
           rewrite > (div_plus_times ? ? ? H5).
           rewrite > (mod_plus_times ? ? ? H5).
-          rewrite > H4.
-          simplify.reflexivity.   
+          reflexivity.   
         ]
       | reflexivity
       ]
@@ -366,8 +364,7 @@ elim n
           rewrite > sym_plus.
           rewrite > (div_plus_times ? ? ? H5).
           rewrite > (mod_plus_times ? ? ? H5).
-          rewrite > H4.
-          simplify.reflexivity.   
+          reflexivity.   
         ]
       | reflexivity
       ]
@@ -619,7 +616,7 @@ elim n
                   rewrite > H8
                   [ reflexivity
                   | assumption
-                  | autobatch
+                  | apply andb_true_true; [2: apply H12]
                   ]
                 | apply eqb_false_to_not_eq.
                   generalize in match H14.
@@ -919,7 +916,7 @@ cut (O < p)
            apply eq_f.
            rewrite > sym_plus.
            apply plus_minus_m_m.
-           autobatch
+           autobatch by le_S_S_to_le, lt_mod_m_m, lt_O_S;
           ]
         ]
       |intros.
@@ -944,8 +941,8 @@ cut (O < p)
         [apply le_S_S_to_le.
          change with ((i/S m) < S n).
          apply (lt_times_to_lt_l m).
-         apply (le_to_lt_to_lt ? i)
-          [autobatch|assumption]
+         apply (le_to_lt_to_lt ? i);[2:assumption]
+         autobatch by eq_plus_to_le, div_mod, lt_O_S.
         |apply le_exp
           [assumption
           |apply le_S_S_to_le.