exercises ready

[helm.git] / helm / software / matita / library / demo / power_derivative.ma

diff --git a/helm/software/matita/library/demo/power_derivative.ma b/helm/software/matita/library/demo/power_derivative.ma
index 76fa66115daa741db40ed4aa04502513da6b9b54..adf85249967c8fe1c402b82dcabbb4839679a44c 100644 (file)
--- a/helm/software/matita/library/demo/power_derivative.ma
+++ b/helm/software/matita/library/demo/power_derivative.ma
@@ -40,11 +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 ≝
@@ -55,7 +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
@@ -88,18 +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 ≝
@@ -108,7 +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.
@@ -245,7 +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.
@@ -268,10 +264,10 @@ theorem derivative_power: ∀n:nat. D[x \sup n] = n·x \sup (pred n).
     case left.
       suppose (0 < m) (m_pos).
       using (S_pred ? m_pos) we proved (m = 1 + pred m) (H1).
-     done.
+     by H1 done.
     case right.
       suppose (0=m) (m_zero). 
-    done.
+    by m_zero, Fmult_zero_f done.
   conclude
      (D[x \sup (1+m)])
    = (D[x · x \sup m]).
@@ -294,8 +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 =