X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdemo%2Fpower_derivative.ma;h=adf85249967c8fe1c402b82dcabbb4839679a44c;hb=79a489c46c77de80979d68a512d1f640f8273f9e;hp=fd58c9564ae12b329e44384d7df14b0b5a07eef0;hpb=9e7db2554d0fd904966c0e6988f1c8763dd15a0b;p=helm.git

diff --git a/helm/software/matita/library/demo/power_derivative.ma b/helm/software/matita/library/demo/power_derivative.ma
index fd58c9564..adf852499 100644
--- a/helm/software/matita/library/demo/power_derivative.ma
+++ b/helm/software/matita/library/demo/power_derivative.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/demo/power_derivative".
-
 include "nat/plus.ma".
 include "nat/orders.ma".
 include "nat/compare.ma".
@@ -42,11 +40,7 @@ interpretation "None" 'one =
 interpretation "Rplus" 'plus x y =
  (cic:/matita/demo/power_derivative/Rplus.con x y).
 
-notation "hvbox(a break \middot b)" 
-  left associative with precedence 55
-for @{ 'times $a $b }.
-
-interpretation "Rmult" 'times x y =
+interpretation "Rmult" 'middot x y =
  (cic:/matita/demo/power_derivative/Rmult.con x y).
 
 definition Fplus ≝
@@ -57,7 +51,7 @@ definition Fmult ≝
 
 interpretation "Fplus" 'plus x y =
  (cic:/matita/demo/power_derivative/Fplus.con x y).
-interpretation "Fmult" 'times x y =
+interpretation "Fmult" 'middot x y =
  (cic:/matita/demo/power_derivative/Fmult.con x y).
 
 notation "2" with precedence 89
@@ -90,18 +84,18 @@ let rec inj (n:nat) on n : R ≝
       ]
   ].
 
-coercion cic:/matita/demo/power_derivative/inj.con.
+coercion inj.
 
 axiom Rplus_Rzero_x: ∀x:R.0+x=x.
 axiom Rplus_comm: symmetric ? Rplus.
 axiom Rplus_assoc: associative ? Rplus.
-axiom Rmult_Rone_x: ∀x:R.1*x=x.
-axiom Rmult_Rzero_x: ∀x:R.0*x=0.
+axiom Rmult_Rone_x: ∀x:R.1 · x=x.
+axiom Rmult_Rzero_x: ∀x:R.0 · x=0.
 axiom Rmult_assoc: associative ? Rmult.
 axiom Rmult_comm: symmetric ? Rmult.
 axiom Rmult_Rplus_distr: distributive ? Rmult Rplus.
 
-alias symbol "times" = "Rmult".
+alias symbol "middot" = "Rmult".
 alias symbol "plus" = "natural plus".
 
 definition monomio ≝
@@ -110,7 +104,7 @@ definition monomio ≝
 definition costante : nat → R → R ≝
  λa:nat.λx:R.inj a.
 
-coercion cic:/matita/demo/power_derivative/costante.con 1.
+coercion costante with 1.
 
 axiom f_eq_extensional:
  ∀f,g:R→R.(∀x:R.f x = g x) → f=g.
@@ -247,7 +241,7 @@ axiom derivative_x0: D[x \sup 0] = 0.
 axiom derivative_x1: D[x] = 1.
 axiom derivative_mult: ∀f,g:R→R. D[f·g] = D[f]·g + f·D[g].
 
-alias symbol "times" = "Fmult".
+alias symbol "middot" = "Fmult".
 
 theorem derivative_power: ∀n:nat. D[x \sup n] = n·x \sup (pred n).
  assume n:nat.
@@ -256,7 +250,6 @@ 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
@@ -265,24 +258,24 @@ 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 _
-     done.
+      using (S_pred ? m_pos) we proved (m = 1 + pred m) (H1).
+     by H1 done.
     case right.
-      suppose (0=m) (m_zero). by _ done.
+      suppose (0=m) (m_zero). 
+    by m_zero, Fmult_zero_f done.
   conclude
      (D[x \sup (1+m)])
    = (D[x · x \sup m]).
    = (D[x] · x \sup m + x · D[x \sup m]).
-   = (x \sup m + x · (m · x \sup (pred 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) by Fmult_one_f Fmult_commutative Fmult_Fplus_distr costante_sum
+   = ((1+m) · x \sup m) timeout=30 by Fmult_one_f, Fmult_commutative, Fmult_Fplus_distr, costante_sum
   done.
 qed.
 
@@ -297,8 +290,7 @@ interpretation "Rderivative" 'derivative \eta.f =
  (cic:/matita/demo/power_derivative/derivative.con f).
 *)
 
-notation "hvbox(\frac 'd' ('d' 'x') break p)"
-  right associative with precedence 90
+notation "hvbox(\frac 'd' ('d' 'x') break p)" with precedence 90
 for @{ 'derivative $p}.
 
 interpretation "Rderivative" 'derivative f =
@@ -310,7 +302,6 @@ 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
@@ -323,7 +314,7 @@ theorem derivative_power': ∀n:nat. D[x \sup (1+n)] = (1+n) · x \sup n.
    = (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)) by Fmult_one_f Fmult_commutative
-     Fmult_Fplus_distr assoc_plus plus_n_SO costante_sum
+   = ((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.