X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdemo%2Fpower_derivative.ma;h=590c5c07ee71f3f21b8b4473c0ce9a0e2189bab6;hb=cb4d4678ada706caaf8c54f2d6780c228645f911;hp=9e59079bd8daf9489fc66a5d1fb1befc3a352ad5;hpb=a180bddcd4a8f35de3d7292162ba05d0077723aa;p=helm.git

diff --git a/helm/software/matita/library/demo/power_derivative.ma b/helm/software/matita/library/demo/power_derivative.ma
index 9e59079bd..590c5c07e 100644
--- a/helm/software/matita/library/demo/power_derivative.ma
+++ b/helm/software/matita/library/demo/power_derivative.ma
@@ -256,7 +256,6 @@ theorem derivative_power: ∀n:nat. 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 _
   done.
  case S (m:nat).
   by induction hypothesis we know
@@ -265,25 +264,24 @@ theorem derivative_power: ∀n:nat. D[x \sup n] = n·x \sup (pred n).
    (D[x \sup (1+m)] = (1+m) · x \sup m).
   we need to prove
    (m · (x \sup (1+ pred m)) = m · x \sup m) (Ppred).
-   by _ we proved (0 < m ∨ 0=m) (cases).
+   we proved (0 < m ∨ 0=m) (cases).
    we proceed by induction on cases
    to prove (m · (x \sup (1+ pred m)) = m · x \sup m).
     case left.
       suppose (0 < m) (m_pos).
-      by (S_pred m m_pos) we proved (m = 1 + pred m) (H1).
-      by _
+      using (S_pred ? m_pos) we proved (m = 1 + pred m) (H1).
      done.
     case right.
-      suppose (0=m) (m_zero). by _ done.
+      suppose (0=m) (m_zero). 
+    done.
   conclude
      (D[x \sup (1+m)])
-   = (D[x · x \sup m]) by _.
-   = (D[x] · x \sup m + x · D[x \sup m]) by _.
-   = (x \sup m + x · (m · x \sup (pred m))) by _.
-clear H.
-   = (x \sup m + m · (x \sup (1 + pred m))) by _.
-   = (x \sup m + m · x \sup m) by _.
-   = ((1+m) · x \sup m) by _ (timeout=30)
+   = (D[x · x \sup m]).
+   = (D[x] · x \sup m + x · D[x \sup m]).
+   = (x \sup m + x · (m · x \sup (pred m))) timeout=30.
+   = (x \sup m + m · (x \sup (1 + pred m))).
+   = (x \sup m + m · x \sup m).
+   = ((1+m) · x \sup m) timeout=30 by Fmult_one_f, Fmult_commutative, Fmult_Fplus_distr, costante_sum
   done.
 qed.
 
@@ -311,7 +309,6 @@ theorem derivative_power': ∀n:nat. D[x \sup (1+n)] = (1+n) · x \sup n.
  (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 _
   done.
  case S (m:nat).
   by induction hypothesis we know
@@ -320,11 +317,11 @@ 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 · 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 _.
-   = (x \sup (1+m) · (costante (2 + m))) by _
+   = (D[x · x \sup (1+m)]).
+   = (D[x] · x \sup (1+m) + x · D[x \sup (1+m)]).
+   = (x \sup (1+m) + x · (costante (1+m) · x \sup m)).
+   = (x \sup (1+m) + costante (1+m) · x \sup (1+m)).
+   = ((2+m) · x \sup (1+m)) timeout=30 by Fmult_one_f, Fmult_commutative,
+       Fmult_Fplus_distr, assoc_plus, plus_n_SO, costante_sum
   done.
-qed.
\ No newline at end of file
+qed.