generalize no more required before elim

diff --git a/helm/software/matita/library/nat/iteration2.ma b/helm/software/matita/library/nat/iteration2.ma
index 752e89b9d02fec375326cd8d8df46b577daaef93..3a4128e70d4727d81aad445bf59036a715b6511d 100644 (file)
--- a/helm/software/matita/library/nat/iteration2.ma
+++ b/helm/software/matita/library/nat/iteration2.ma
@@ -286,17 +286,16 @@ theorem le_sigma_p:
 (\forall i. i < n \to p i = true \to g1 i \le g2 i ) \to 
 sigma_p n p g1 \le sigma_p n p g2.
 intros.
-generalize in match H.
-elim n
+elim n in H ⊢ %
   [apply le_n.
   |apply (bool_elim ? (p n1));intros
     [rewrite > true_to_sigma_p_Sn
       [rewrite > true_to_sigma_p_Sn in ⊢ (? ? %)
         [apply le_plus
-          [apply H2[apply le_n|assumption]
-          |apply H1.
+          [apply H1[apply le_n|assumption]
+          |apply H.
            intros.
-           apply H2[apply le_S.assumption|assumption]
+           apply H1[apply le_S.assumption|assumption]
           ]
         |assumption
         ]
@@ -304,9 +303,9 @@ elim n
       ]
     |rewrite > false_to_sigma_p_Sn
       [rewrite > false_to_sigma_p_Sn in ⊢ (? ? %)
-        [apply H1.
+        [apply H.
          intros.
-         apply H2[apply le_S.assumption|assumption]
+         apply H1[apply le_S.assumption|assumption]
         |assumption
         ]
       |assumption
@@ -322,25 +321,24 @@ theorem le_sigma_p1:
 bool_to_nat (p1 i)*(g1 i) \le bool_to_nat (p2 i)*g2 i) \to 
 sigma_p n p1 g1 \le sigma_p n p2 g2.
 intros.
-generalize in match H.
-elim n
+elim n in H ⊢ %
   [apply le_n.
   |apply (bool_elim ? (p1 n1));intros
     [apply (bool_elim ? (p2 n1));intros
       [rewrite > true_to_sigma_p_Sn
         [rewrite > true_to_sigma_p_Sn in ⊢ (? ? %)
           [apply le_plus
-            [lapply (H2 n1) as H5
-              [rewrite > H3 in H5.
-               rewrite > H4 in H5.
+            [lapply (H1 n1) as H5
+              [rewrite > H2 in H5.
+               rewrite > H3 in H5.
                simplify in H5.
                rewrite < plus_n_O in H5.
                rewrite < plus_n_O in H5.
                assumption
               |apply le_S_S.apply le_n
               ]
-            |apply H1.intros.
-             apply H2.apply le_S.assumption
+            |apply H.intros.
+             apply H1.apply le_S.assumption
             ]
           |assumption
           ]
@@ -350,16 +348,16 @@ elim n
         [rewrite > false_to_sigma_p_Sn in ⊢ (? ? %)
           [change in ⊢ (? ? %) with (O + sigma_p n1 p2 g2).
            apply le_plus
-            [lapply (H2 n1) as H5
-              [rewrite > H3 in H5.
-               rewrite > H4 in H5.
+            [lapply (H1 n1) as H5
+              [rewrite > H2 in H5.
+               rewrite > H3 in H5.
                simplify in H5.
                rewrite < plus_n_O in H5.
                assumption
               |apply le_S_S.apply le_n
               ]
-            |apply H1.intros.
-             apply H2.apply le_S.assumption
+            |apply H.intros.
+             apply H1.apply le_S.assumption
             ]
           |assumption
           ]
@@ -371,16 +369,16 @@ elim n
         [rewrite > true_to_sigma_p_Sn in ⊢ (? ? %)
           [change in ⊢ (? % ?) with (O + sigma_p n1 p1 g1).
            apply le_plus
-            [lapply (H2 n1) as H5
-              [rewrite > H3 in H5.
-               rewrite > H4 in H5.
+            [lapply (H1 n1) as H5
+              [rewrite > H2 in H5.
+               rewrite > H3 in H5.
                simplify in H5.
                rewrite < plus_n_O in H5.
                assumption
               |apply le_S_S.apply le_n
               ]
-            |apply H1.intros.
-             apply H2.apply le_S.assumption
+            |apply H.intros.
+             apply H1.apply le_S.assumption
             ]
           |assumption
           ]
@@ -388,8 +386,8 @@ elim n
         ]
       |rewrite > false_to_sigma_p_Sn
         [rewrite > false_to_sigma_p_Sn in ⊢ (? ? %)
-          [apply H1.intros.
-           apply H2.apply le_S.assumption
+          [apply H.intros.
+           apply H1.apply le_S.assumption
           |assumption
           ]
         |assumption
@@ -397,7 +395,7 @@ elim n
       ]
     ]
   ]
-qed.    
+qed.
 
 theorem lt_sigma_p: 
 \forall n:nat. \forall p:nat \to bool. \forall g1,g2:nat \to nat.

diff --git a/helm/software/matita/library/nat/minimization.ma b/helm/software/matita/library/nat/minimization.ma
index bc2cc70591a3de6e10d5d1f4604e5958046a32d6..5b1552dc6777de3c1a9ef298b846b62796af70ff 100644 (file)
--- a/helm/software/matita/library/nat/minimization.ma
+++ b/helm/software/matita/library/nat/minimization.ma
@@ -236,17 +236,16 @@ intros 2.
 elim n.absurd (le m O).assumption.
 cut (O < m).apply (lt_O_n_elim m Hcut).exact not_le_Sn_O.
 rewrite < (max_O_f f).assumption.
-generalize in match H1.
-elim (max_S_max f n1).
-elim H3.
+elim (max_S_max f n1) in H1 ⊢ %.
+elim H1.
 absurd (m \le S n1).assumption.
-apply lt_to_not_le.rewrite < H6.assumption.
-elim H3.
+apply lt_to_not_le.rewrite < H5.assumption.
+elim H1.
 apply (le_n_Sm_elim m n1 H2).
 intro.
-apply H.rewrite < H6.assumption.
+apply H.rewrite < H5.assumption.
 apply le_S_S_to_le.assumption.
-intro.rewrite > H7.assumption.
+intro.rewrite > H6.assumption.
 qed.
 
 theorem f_false_to_le_max: \forall f,n,p. (∃i:nat.i≤n∧f i=true) \to
@@ -385,7 +384,7 @@ qed.
 theorem lt_min_aux_to_false : \forall f:nat \to bool. 
 \forall n,off,m:nat. n \leq m \to m < (min_aux off n f) \to f m = false.
 intros 3.
-generalize in match n; clear n.
+generalize in match n; clear n;
 elim off.absurd (le n1 m).assumption.
 apply lt_to_not_le.rewrite < (min_aux_O_f f n1).assumption.
 elim (le_to_or_lt_eq ? ? H1);
@@ -422,8 +421,7 @@ qed.
 lemma le_min_aux : \forall f:nat \to bool. 
 \forall n,off:nat. n \leq (min_aux off n f).
 intros 3.
-generalize in match n. clear n.
-elim off.
+elim off in n ⊢ %.
 rewrite > (min_aux_O_f f n1).apply le_n.
 elim (min_aux_S f n n1).
 elim H1.rewrite > H3.apply le_n.
@@ -437,8 +435,7 @@ qed.
 theorem le_min_aux_r : \forall f:nat \to bool. 
 \forall n,off:nat. (min_aux off n f) \le n+off.
 intros.
-generalize in match n. clear n.
-elim off.simplify.
+elim off in n ⊢ %.simplify.
 elim (f n1).simplify.rewrite < plus_n_O.apply le_n.
 simplify.rewrite < plus_n_O.apply le_n.
 simplify.elim (f n1).