Release 0.5.9.

[helm.git] / helm / software / matita / contribs / ng_assembly / common / ascii_lemmas.ma

diff --git a/helm/software/matita/contribs/ng_assembly/common/ascii_lemmas.ma b/helm/software/matita/contribs/ng_assembly/common/ascii_lemmas.ma
index fff2c748b89b841cf740b299b2ceac0a9809bb2a..0d10de49d991db9e1f776c095a70c4c3e63de9cd 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/common/ascii_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/common/ascii_lemmas.ma
@@ -16,7 +16,7 @@
 (*                          Progetto FreeScale                            *)
 (*                                                                        *)
 (*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
-(*   Sviluppo: 2008-2010                                                  *)
+(*   Ultima modifica: 05/08/2009                                          *)
 (*                                                                        *)
 (* ********************************************************************** *)
 
@@ -27,7 +27,6 @@ include "num/bool_lemmas.ma".
 (* DEFINIZIONE ASCII MINIMALE *)
 (* ************************** *)
 
-(*
 ndefinition ascii_destruct_aux ≝
 Πc1,c2.ΠP:Prop.c1 = c2 →
  match eq_ascii c1 c2 with [ true ⇒ P → P | false ⇒ P ].
@@ -39,7 +38,6 @@ nlemma ascii_destruct : ascii_destruct_aux.
  nnormalize;
  napply (λx.x).
 nqed.
-*)
 
 nlemma eq_to_eqascii : ∀n1,n2.n1 = n2 → eq_ascii n1 n2 = true.
  #n1; #n2; #H;
@@ -57,8 +55,105 @@ nlemma neqascii_to_neq : ∀n1,n2.eq_ascii n1 n2 = false → n1 ≠ n2.
  ##]
 nqed.
 
-(* !!! per brevita... *)
-naxiom eqascii_to_eq : ∀c1,c2.eq_ascii c1 c2 = true → c1 = c2.
+nlemma eqascii_to_eq1 : ∀a2.eq_ascii ch_0 a2 = true → ch_0 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##1: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq2 : ∀a2.eq_ascii ch_1 a2 = true → ch_1 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##2: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq3 : ∀a2.eq_ascii ch_2 a2 = true → ch_2 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##3: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq4 : ∀a2.eq_ascii ch_3 a2 = true → ch_3 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##4: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq5 : ∀a2.eq_ascii ch_4 a2 = true → ch_4 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##5: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq6 : ∀a2.eq_ascii ch_5 a2 = true → ch_5 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##6: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq7 : ∀a2.eq_ascii ch_6 a2 = true → ch_6 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##7: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq8 : ∀a2.eq_ascii ch_7 a2 = true → ch_7 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##8: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq9 : ∀a2.eq_ascii ch_8 a2 = true → ch_8 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##9: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq10 : ∀a2.eq_ascii ch_9 a2 = true → ch_9 = a2. #a2; ncases a2; nnormalize; #H; ##[ ##10: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq11 : ∀a2.eq_ascii ch__ a2 = true → ch__ = a2. #a2; ncases a2; nnormalize; #H; ##[ ##11: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq12 : ∀a2.eq_ascii ch_A a2 = true → ch_A = a2. #a2; ncases a2; nnormalize; #H; ##[ ##12: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq13 : ∀a2.eq_ascii ch_B a2 = true → ch_B = a2. #a2; ncases a2; nnormalize; #H; ##[ ##13: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq14 : ∀a2.eq_ascii ch_C a2 = true → ch_C = a2. #a2; ncases a2; nnormalize; #H; ##[ ##14: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq15 : ∀a2.eq_ascii ch_D a2 = true → ch_D = a2. #a2; ncases a2; nnormalize; #H; ##[ ##15: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq16 : ∀a2.eq_ascii ch_E a2 = true → ch_E = a2. #a2; ncases a2; nnormalize; #H; ##[ ##16: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq17 : ∀a2.eq_ascii ch_F a2 = true → ch_F = a2. #a2; ncases a2; nnormalize; #H; ##[ ##17: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq18 : ∀a2.eq_ascii ch_G a2 = true → ch_G = a2. #a2; ncases a2; nnormalize; #H; ##[ ##18: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq19 : ∀a2.eq_ascii ch_H a2 = true → ch_H = a2. #a2; ncases a2; nnormalize; #H; ##[ ##19: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq20 : ∀a2.eq_ascii ch_I a2 = true → ch_I = a2. #a2; ncases a2; nnormalize; #H; ##[ ##20: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq21 : ∀a2.eq_ascii ch_J a2 = true → ch_J = a2. #a2; ncases a2; nnormalize; #H; ##[ ##21: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq22 : ∀a2.eq_ascii ch_K a2 = true → ch_K = a2. #a2; ncases a2; nnormalize; #H; ##[ ##22: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq23 : ∀a2.eq_ascii ch_L a2 = true → ch_L = a2. #a2; ncases a2; nnormalize; #H; ##[ ##23: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq24 : ∀a2.eq_ascii ch_M a2 = true → ch_M = a2. #a2; ncases a2; nnormalize; #H; ##[ ##24: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq25 : ∀a2.eq_ascii ch_N a2 = true → ch_N = a2. #a2; ncases a2; nnormalize; #H; ##[ ##25: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq26 : ∀a2.eq_ascii ch_O a2 = true → ch_O = a2. #a2; ncases a2; nnormalize; #H; ##[ ##26: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq27 : ∀a2.eq_ascii ch_P a2 = true → ch_P = a2. #a2; ncases a2; nnormalize; #H; ##[ ##27: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq28 : ∀a2.eq_ascii ch_Q a2 = true → ch_Q = a2. #a2; ncases a2; nnormalize; #H; ##[ ##28: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq29 : ∀a2.eq_ascii ch_R a2 = true → ch_R = a2. #a2; ncases a2; nnormalize; #H; ##[ ##29: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq30 : ∀a2.eq_ascii ch_S a2 = true → ch_S = a2. #a2; ncases a2; nnormalize; #H; ##[ ##30: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq31 : ∀a2.eq_ascii ch_T a2 = true → ch_T = a2. #a2; ncases a2; nnormalize; #H; ##[ ##31: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq32 : ∀a2.eq_ascii ch_U a2 = true → ch_U = a2. #a2; ncases a2; nnormalize; #H; ##[ ##32: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq33 : ∀a2.eq_ascii ch_V a2 = true → ch_V = a2. #a2; ncases a2; nnormalize; #H; ##[ ##33: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq34 : ∀a2.eq_ascii ch_W a2 = true → ch_W = a2. #a2; ncases a2; nnormalize; #H; ##[ ##34: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq35 : ∀a2.eq_ascii ch_X a2 = true → ch_X = a2. #a2; ncases a2; nnormalize; #H; ##[ ##35: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq36 : ∀a2.eq_ascii ch_Y a2 = true → ch_Y = a2. #a2; ncases a2; nnormalize; #H; ##[ ##36: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq37 : ∀a2.eq_ascii ch_Z a2 = true → ch_Z = a2. #a2; ncases a2; nnormalize; #H; ##[ ##37: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq38 : ∀a2.eq_ascii ch_a a2 = true → ch_a = a2. #a2; ncases a2; nnormalize; #H; ##[ ##38: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq39 : ∀a2.eq_ascii ch_b a2 = true → ch_b = a2. #a2; ncases a2; nnormalize; #H; ##[ ##39: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq40 : ∀a2.eq_ascii ch_c a2 = true → ch_c = a2. #a2; ncases a2; nnormalize; #H; ##[ ##40: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq41 : ∀a2.eq_ascii ch_d a2 = true → ch_d = a2. #a2; ncases a2; nnormalize; #H; ##[ ##41: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq42 : ∀a2.eq_ascii ch_e a2 = true → ch_e = a2. #a2; ncases a2; nnormalize; #H; ##[ ##42: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq43 : ∀a2.eq_ascii ch_f a2 = true → ch_f = a2. #a2; ncases a2; nnormalize; #H; ##[ ##43: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq44 : ∀a2.eq_ascii ch_g a2 = true → ch_g = a2. #a2; ncases a2; nnormalize; #H; ##[ ##44: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq45 : ∀a2.eq_ascii ch_h a2 = true → ch_h = a2. #a2; ncases a2; nnormalize; #H; ##[ ##45: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq46 : ∀a2.eq_ascii ch_i a2 = true → ch_i = a2. #a2; ncases a2; nnormalize; #H; ##[ ##46: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq47 : ∀a2.eq_ascii ch_j a2 = true → ch_j = a2. #a2; ncases a2; nnormalize; #H; ##[ ##47: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq48 : ∀a2.eq_ascii ch_k a2 = true → ch_k = a2. #a2; ncases a2; nnormalize; #H; ##[ ##48: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq49 : ∀a2.eq_ascii ch_l a2 = true → ch_l = a2. #a2; ncases a2; nnormalize; #H; ##[ ##49: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq50 : ∀a2.eq_ascii ch_m a2 = true → ch_m = a2. #a2; ncases a2; nnormalize; #H; ##[ ##50: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq51 : ∀a2.eq_ascii ch_n a2 = true → ch_n = a2. #a2; ncases a2; nnormalize; #H; ##[ ##51: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq52 : ∀a2.eq_ascii ch_o a2 = true → ch_o = a2. #a2; ncases a2; nnormalize; #H; ##[ ##52: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq53 : ∀a2.eq_ascii ch_p a2 = true → ch_p = a2. #a2; ncases a2; nnormalize; #H; ##[ ##53: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq54 : ∀a2.eq_ascii ch_q a2 = true → ch_q = a2. #a2; ncases a2; nnormalize; #H; ##[ ##54: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq55 : ∀a2.eq_ascii ch_r a2 = true → ch_r = a2. #a2; ncases a2; nnormalize; #H; ##[ ##55: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq56 : ∀a2.eq_ascii ch_s a2 = true → ch_s = a2. #a2; ncases a2; nnormalize; #H; ##[ ##56: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq57 : ∀a2.eq_ascii ch_t a2 = true → ch_t = a2. #a2; ncases a2; nnormalize; #H; ##[ ##57: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq58 : ∀a2.eq_ascii ch_u a2 = true → ch_u = a2. #a2; ncases a2; nnormalize; #H; ##[ ##58: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq59 : ∀a2.eq_ascii ch_v a2 = true → ch_v = a2. #a2; ncases a2; nnormalize; #H; ##[ ##59: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq60 : ∀a2.eq_ascii ch_w a2 = true → ch_w = a2. #a2; ncases a2; nnormalize; #H; ##[ ##60: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq61 : ∀a2.eq_ascii ch_x a2 = true → ch_x = a2. #a2; ncases a2; nnormalize; #H; ##[ ##61: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq62 : ∀a2.eq_ascii ch_y a2 = true → ch_y = a2. #a2; ncases a2; nnormalize; #H; ##[ ##62: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqascii_to_eq63 : ∀a2.eq_ascii ch_z a2 = true → ch_z = a2. #a2; ncases a2; nnormalize; #H; ##[ ##63: napply refl_eq | ##*: napply (bool_destruct … H) ##] nqed.
+
+nlemma eqascii_to_eq : ∀c1,c2.eq_ascii c1 c2 = true → c1 = c2.
+ #c1; ncases c1;
+ ##[ ##1: napply eqascii_to_eq1 ##| ##2: napply eqascii_to_eq2
+ ##| ##3: napply eqascii_to_eq3 ##| ##4: napply eqascii_to_eq4
+ ##| ##5: napply eqascii_to_eq5 ##| ##6: napply eqascii_to_eq6
+ ##| ##7: napply eqascii_to_eq7 ##| ##8: napply eqascii_to_eq8 
+ ##| ##9: napply eqascii_to_eq9 ##| ##10: napply eqascii_to_eq10
+ ##| ##11: napply eqascii_to_eq11 ##| ##12: napply eqascii_to_eq12 
+ ##| ##13: napply eqascii_to_eq13 ##| ##14: napply eqascii_to_eq14 
+ ##| ##15: napply eqascii_to_eq15 ##| ##16: napply eqascii_to_eq16 
+ ##| ##17: napply eqascii_to_eq17 ##| ##18: napply eqascii_to_eq18
+ ##| ##19: napply eqascii_to_eq19 ##| ##20: napply eqascii_to_eq20 
+ ##| ##21: napply eqascii_to_eq21 ##| ##22: napply eqascii_to_eq22 
+ ##| ##23: napply eqascii_to_eq23 ##| ##24: napply eqascii_to_eq24 
+ ##| ##25: napply eqascii_to_eq25 ##| ##26: napply eqascii_to_eq26
+ ##| ##27: napply eqascii_to_eq27 ##| ##28: napply eqascii_to_eq28
+ ##| ##29: napply eqascii_to_eq29 ##| ##30: napply eqascii_to_eq30 
+ ##| ##31: napply eqascii_to_eq31 ##| ##32: napply eqascii_to_eq32 
+ ##| ##33: napply eqascii_to_eq33 ##| ##34: napply eqascii_to_eq34
+ ##| ##35: napply eqascii_to_eq35 ##| ##36: napply eqascii_to_eq36
+ ##| ##37: napply eqascii_to_eq37 ##| ##38: napply eqascii_to_eq38
+ ##| ##39: napply eqascii_to_eq39 ##| ##40: napply eqascii_to_eq40
+ ##| ##41: napply eqascii_to_eq41 ##| ##42: napply eqascii_to_eq42
+ ##| ##43: napply eqascii_to_eq43 ##| ##44: napply eqascii_to_eq44 
+ ##| ##45: napply eqascii_to_eq45 ##| ##46: napply eqascii_to_eq46
+ ##| ##47: napply eqascii_to_eq47 ##| ##48: napply eqascii_to_eq48 
+ ##| ##49: napply eqascii_to_eq49 ##| ##50: napply eqascii_to_eq50
+ ##| ##51: napply eqascii_to_eq51 ##| ##52: napply eqascii_to_eq52
+ ##| ##53: napply eqascii_to_eq53 ##| ##54: napply eqascii_to_eq54 
+ ##| ##55: napply eqascii_to_eq55 ##| ##56: napply eqascii_to_eq56
+ ##| ##57: napply eqascii_to_eq57 ##| ##58: napply eqascii_to_eq58
+ ##| ##59: napply eqascii_to_eq59 ##| ##60: napply eqascii_to_eq60 
+ ##| ##61: napply eqascii_to_eq61 ##| ##62: napply eqascii_to_eq62 
+ ##| ##63: napply eqascii_to_eq63 ##]
+nqed.
 
 nlemma neq_to_neqascii : ∀n1,n2.n1 ≠ n2 → eq_ascii n1 n2 = false.
  #n1; #n2; #H;