- init_cache_and_tables rewritten using the automation_cache

[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 590c5c07ee71f3f21b8b4473c0ce9a0e2189bab6..10cb21835790765e9e7fe64e39bd5b3f862251fb 100644 (file)
--- 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".
@@ -26,28 +24,17 @@ axiom Rmult: R→R→R.
 
 notation "0" with precedence 89
 for @{ 'zero }.
-interpretation "Rzero" 'zero =
- (cic:/matita/demo/power_derivative/R0.con).
-interpretation "Nzero" 'zero =
- (cic:/matita/nat/nat/nat.ind#xpointer(1/1/1)).
+interpretation "Rzero" 'zero = (R0).
+interpretation "Nzero" 'zero = (O).
 
 notation "1" with precedence 89
 for @{ 'one }.
-interpretation "Rone" 'one =
- (cic:/matita/demo/power_derivative/R1.con).
-interpretation "None" 'one =
- (cic:/matita/nat/nat/nat.ind#xpointer(1/1/2)
-   cic:/matita/nat/nat/nat.ind#xpointer(1/1/1)).
-
-interpretation "Rplus" 'plus x y =
- (cic:/matita/demo/power_derivative/Rplus.con x y).
+interpretation "Rone" 'one = (R1).
+interpretation "None" 'one = (S O).
 
-notation "hvbox(a break \middot b)" 
-  left associative with precedence 55
-for @{ 'times $a $b }.
+interpretation "Rplus" 'plus x y = (Rplus x y).
 
-interpretation "Rmult" 'times x y =
- (cic:/matita/demo/power_derivative/Rmult.con x y).
+interpretation "Rmult" 'middot x y = (Rmult x y).
 
 definition Fplus ≝
  λf,g:R→R.λx:R.f x + g x.
@@ -55,21 +42,13 @@ definition Fplus ≝
 definition Fmult ≝
  λf,g:R→R.λx:R.f x · g x.
 
-interpretation "Fplus" 'plus x y =
- (cic:/matita/demo/power_derivative/Fplus.con x y).
-interpretation "Fmult" 'times x y =
- (cic:/matita/demo/power_derivative/Fmult.con x y).
+interpretation "Fplus" 'plus x y = (Fplus x y).
+interpretation "Fmult" 'middot x y = (Fmult x y).
 
 notation "2" with precedence 89
 for @{ 'two }.
-interpretation "Rtwo" 'two =
- (cic:/matita/demo/power_derivative/Rplus.con
-   cic:/matita/demo/power_derivative/R1.con
-   cic:/matita/demo/power_derivative/R1.con).
-interpretation "Ntwo" 'two =
- (cic:/matita/nat/nat/nat.ind#xpointer(1/1/2)
-   (cic:/matita/nat/nat/nat.ind#xpointer(1/1/2)
-     (cic:/matita/nat/nat/nat.ind#xpointer(1/1/1)))).
+interpretation "Rtwo" 'two = (Rplus R1 R1).
+interpretation "Ntwo" 'two = (S (S O)).
 
 let rec Rpower (x:R) (n:nat) on n ≝
  match n with
@@ -77,8 +56,7 @@ let rec Rpower (x:R) (n:nat) on n ≝
   | S n ⇒ x · (Rpower x n)
   ].
 
-interpretation "Rpower" 'exp x n =
- (cic:/matita/demo/power_derivative/Rpower.con x n).
+interpretation "Rpower" 'exp x n = (Rpower x n).
 
 let rec inj (n:nat) on n : R ≝
  match n with
@@ -90,18 +68,18 @@ 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 +88,7 @@ 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.
@@ -229,8 +207,7 @@ notation "hvbox('D'[f])"
   non associative with precedence 90
 for @{ 'derivative $f }.
 
-interpretation "Rderivative" 'derivative f =
- (cic:/matita/demo/power_derivative/derivative.con f).
+interpretation "Rderivative" 'derivative f = (derivative f).
 
 notation "hvbox('x' \sup n)"
   non associative with precedence 60
@@ -240,14 +217,13 @@ notation "hvbox('x')"
   non associative with precedence 60
 for @{ 'monomio 1 }.
 
-interpretation "Rmonomio" 'monomio n =
- (cic:/matita/demo/power_derivative/monomio.con n).
+interpretation "Rmonomio" 'monomio n = (monomio n).
 
 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.
@@ -270,10 +246,10 @@ 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]).
@@ -292,16 +268,13 @@ for @{ 'derivative ${default
   @{\lambda ${ident i} : $ty. $p)}
   @{\lambda ${ident i} . $p}}}.
 
-interpretation "Rderivative" 'derivative \eta.f =
- (cic:/matita/demo/power_derivative/derivative.con f).
+interpretation "Rderivative" 'derivative \eta.f = (derivative 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 =
- (cic:/matita/demo/power_derivative/derivative.con f).
+interpretation "Rderivative" 'derivative f = (derivative f).
 
 theorem derivative_power': ∀n:nat. D[x \sup (1+n)] = (1+n) · x \sup n.
  assume n:nat.