X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdemo%2Fpower_derivative.ma;h=9e59079bd8daf9489fc66a5d1fb1befc3a352ad5;hb=3ed7d56cf4fab7401f8b400c45b2e35579ba71dd;hp=24656c1d3da9f53f43d170b4837cc765ce1fb138;hpb=45d8e093b732768f58794dc3169e2980257dc7d3;p=helm.git

diff --git a/helm/software/matita/library/demo/power_derivative.ma b/helm/software/matita/library/demo/power_derivative.ma
index 24656c1d3..9e59079bd 100644
--- a/helm/software/matita/library/demo/power_derivative.ma
+++ b/helm/software/matita/library/demo/power_derivative.ma
@@ -121,7 +121,7 @@ lemma Fmult_one_f: ∀f:R→R.1·f=f.
  simplify;
  apply f_eq_extensional;
  intro;
- auto.
+ autobatch.
 qed.
 
 lemma Fmult_zero_f: ∀f:R→R.0·f=0.
@@ -130,7 +130,7 @@ lemma Fmult_zero_f: ∀f:R→R.0·f=0.
  simplify;
  apply f_eq_extensional;
  intro;
- auto.
+ autobatch.
 qed.
 
 lemma Fmult_commutative: symmetric ? Fmult.
@@ -139,7 +139,7 @@ lemma Fmult_commutative: symmetric ? Fmult.
  unfold Fmult;
  apply f_eq_extensional;
  intros;
- auto.
+ autobatch.
 qed.
 
 lemma Fmult_associative: associative ? Fmult.
@@ -149,7 +149,7 @@ lemma Fmult_associative: associative ? Fmult.
  unfold Fmult;
  apply f_eq_extensional;
  intros;
- auto.
+ autobatch.
 qed.
 
 lemma Fmult_Fplus_distr: distributive ? Fmult Fplus.
@@ -160,7 +160,7 @@ lemma Fmult_Fplus_distr: distributive ? Fmult Fplus.
  apply f_eq_extensional;
  intros;
  simplify;
- auto.
+ autobatch.
 qed.
 
 lemma monomio_product:
@@ -173,13 +173,13 @@ lemma monomio_product:
   [ simplify;
     apply f_eq_extensional;
     intro;
-    auto
+    autobatch
   | simplify;
     apply f_eq_extensional;
     intro;
     cut (x\sup (n1+m) = x \sup n1 · x \sup m);
      [ rewrite > Hcut;
-       auto
+       autobatch
      | change in ⊢ (? ? % ?) with ((λx:R.x\sup(n1+m)) x);
        rewrite > H;
        reflexivity
@@ -196,7 +196,7 @@ lemma costante_sum:
  intros;
  elim n;
   [ simplify;
-    auto
+    autobatch
   | simplify;
     clear x;
     clear H;
@@ -205,19 +205,19 @@ lemma costante_sum:
      [ simplify;
        elim m;
         [ simplify;
-          auto
+          autobatch
         | simplify;
           rewrite < H;
-          auto
+          autobatch
         ]
      | simplify;
        rewrite < H;
        clear H;
        elim n;
         [ simplify;
-          auto
+          autobatch
         | simplify;
-          auto
+          autobatch
         ]
      ]
    ].
@@ -251,8 +251,9 @@ alias symbol "times" = "Fmult".
 
 theorem derivative_power: ∀n:nat. D[x \sup n] = n·x \sup (pred n).
  assume n:nat.
- we proceed by induction on n to prove
- (D[x \sup n] = n · x \sup (pred n)).
+ (*we proceed by induction on n to prove
+ (D[x \sup n] = n · x \sup (pred n)).*)
+ elim n 0.
  case O.
    the thesis becomes (D[x \sup 0] = 0·x \sup (pred 0)).
    by _
@@ -306,8 +307,8 @@ interpretation "Rderivative" 'derivative f =
 
 theorem derivative_power': ∀n:nat. D[x \sup (1+n)] = (1+n) · x \sup n.
  assume n:nat.
- we proceed by induction on n to prove
- (D[x \sup (1+n)] = (1+n) · x \sup n).
+ (*we proceed by induction on n to prove
+ (D[x \sup (1+n)] = (1+n) · x \sup n).*) elim n 0.
  case O.
    the thesis becomes (D[x \sup 1] = 1 · x \sup 0).
    by _
@@ -319,8 +320,8 @@ theorem derivative_power': ∀n:nat. D[x \sup (1+n)] = (1+n) · x \sup n.
    (D[x \sup (2+m)] = (2+m) · x \sup (1+m)).
   conclude
      (D[x \sup (2+m)])
-   = (D[x \sup 1 · x \sup (1+m)]) by _.
-   = (D[x \sup 1] · x \sup (1+m) + x · D[x \sup (1+m)]) by _.
+   = (D[x · x \sup (1+m)]) by _.
+   = (D[x] · x \sup (1+m) + x · D[x \sup (1+m)]) by _.
    = (x \sup (1+m) + x · (costante (1+m) · x \sup m)) by _.
 clear H.
    = (x \sup (1+m) + costante (1+m) · x \sup (1+m)) by _.