Release 0.5.9.

[helm.git] / helm / software / matita / contribs / ng_assembly / num / bitrigesim_lemmas.ma

diff --git a/helm/software/matita/contribs/ng_assembly/num/bitrigesim_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/bitrigesim_lemmas.ma
index 9aa485cc5f1c846d16c8e32547d9d5b90a97a1c8..5eecaff9160d2ec82a5eb69b683aa96bb77987ce 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/num/bitrigesim_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/bitrigesim_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".
 (* BITRIGESIMALI *)
 (* ************* *)
 
-(*
 ndefinition bitrigesim_destruct_aux ≝
 Πt1,t2:bitrigesim.ΠP:Prop.t1 = t2 →
  match eq_bit t1 t2 with [ true ⇒ P → P | false ⇒ P ].
@@ -39,7 +38,6 @@ ndefinition bitrigesim_destruct : bitrigesim_destruct_aux.
  nnormalize;
  napply (λx.x).
 nqed.
-*)
 
 nlemma eq_to_eqbit : ∀n1,n2.n1 = n2 → eq_bit n1 n2 = true.
  #n1; #n2; #H;
@@ -57,8 +55,59 @@ nlemma neqbit_to_neq : ∀n1,n2.eq_bit n1 n2 = false → n1 ≠ n2.
  ##]
 nqed.
 
-(* !!! per brevita... *)
-naxiom eqbit_to_eq : ∀t1,t2.eq_bit t1 t2 = true → t1 = t2.
+nlemma eqbit_to_eq1 : ∀t2.eq_bit t00 t2 = true → t00 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##1: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq2 : ∀t2.eq_bit t01 t2 = true → t01 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##2: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq3 : ∀t2.eq_bit t02 t2 = true → t02 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##3: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq4 : ∀t2.eq_bit t03 t2 = true → t03 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##4: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq5 : ∀t2.eq_bit t04 t2 = true → t04 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##5: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq6 : ∀t2.eq_bit t05 t2 = true → t05 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##6: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq7 : ∀t2.eq_bit t06 t2 = true → t06 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##7: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq8 : ∀t2.eq_bit t07 t2 = true → t07 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##8: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq9 : ∀t2.eq_bit t08 t2 = true → t08 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##9: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq10 : ∀t2.eq_bit t09 t2 = true → t09 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##10: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq11 : ∀t2.eq_bit t0A t2 = true → t0A = t2. #t2; ncases t2; nnormalize; #H; ##[ ##11: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq12 : ∀t2.eq_bit t0B t2 = true → t0B = t2. #t2; ncases t2; nnormalize; #H; ##[ ##12: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq13 : ∀t2.eq_bit t0C t2 = true → t0C = t2. #t2; ncases t2; nnormalize; #H; ##[ ##13: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq14 : ∀t2.eq_bit t0D t2 = true → t0D = t2. #t2; ncases t2; nnormalize; #H; ##[ ##14: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq15 : ∀t2.eq_bit t0E t2 = true → t0E = t2. #t2; ncases t2; nnormalize; #H; ##[ ##15: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq16 : ∀t2.eq_bit t0F t2 = true → t0F = t2. #t2; ncases t2; nnormalize; #H; ##[ ##16: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq17 : ∀t2.eq_bit t10 t2 = true → t10 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##17: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq18 : ∀t2.eq_bit t11 t2 = true → t11 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##18: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq19 : ∀t2.eq_bit t12 t2 = true → t12 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##19: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq20 : ∀t2.eq_bit t13 t2 = true → t13 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##20: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq21 : ∀t2.eq_bit t14 t2 = true → t14 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##21: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq22 : ∀t2.eq_bit t15 t2 = true → t15 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##22: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq23 : ∀t2.eq_bit t16 t2 = true → t16 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##23: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq24 : ∀t2.eq_bit t17 t2 = true → t17 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##24: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq25 : ∀t2.eq_bit t18 t2 = true → t18 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##25: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq26 : ∀t2.eq_bit t19 t2 = true → t19 = t2. #t2; ncases t2; nnormalize; #H; ##[ ##26: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq27 : ∀t2.eq_bit t1A t2 = true → t1A = t2. #t2; ncases t2; nnormalize; #H; ##[ ##27: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq28 : ∀t2.eq_bit t1B t2 = true → t1B = t2. #t2; ncases t2; nnormalize; #H; ##[ ##28: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq29 : ∀t2.eq_bit t1C t2 = true → t1C = t2. #t2; ncases t2; nnormalize; #H; ##[ ##29: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq30 : ∀t2.eq_bit t1D t2 = true → t1D = t2. #t2; ncases t2; nnormalize; #H; ##[ ##30: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq31 : ∀t2.eq_bit t1E t2 = true → t1E = t2. #t2; ncases t2; nnormalize; #H; ##[ ##31: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+nlemma eqbit_to_eq32 : ∀t2.eq_bit t1F t2 = true → t1F = t2. #t2; ncases t2; nnormalize; #H; ##[ ##32: napply refl_eq ##| ##*: napply (bool_destruct … H) ##] nqed.
+
+nlemma eqbit_to_eq : ∀t1,t2.eq_bit t1 t2 = true → t1 = t2.
+ #t1; ncases t1;
+ ##[ ##1: napply eqbit_to_eq1 ##| ##2: napply eqbit_to_eq2
+ ##| ##3: napply eqbit_to_eq3 ##| ##4: napply eqbit_to_eq4
+ ##| ##5: napply eqbit_to_eq5 ##| ##6: napply eqbit_to_eq6
+ ##| ##7: napply eqbit_to_eq7 ##| ##8: napply eqbit_to_eq8
+ ##| ##9: napply eqbit_to_eq9 ##| ##10: napply eqbit_to_eq10
+ ##| ##11: napply eqbit_to_eq11 ##| ##12: napply eqbit_to_eq12
+ ##| ##13: napply eqbit_to_eq13 ##| ##14: napply eqbit_to_eq14
+ ##| ##15: napply eqbit_to_eq15 ##| ##16: napply eqbit_to_eq16
+ ##| ##17: napply eqbit_to_eq17 ##| ##18: napply eqbit_to_eq18
+ ##| ##19: napply eqbit_to_eq19 ##| ##20: napply eqbit_to_eq20
+ ##| ##21: napply eqbit_to_eq21 ##| ##22: napply eqbit_to_eq22
+ ##| ##23: napply eqbit_to_eq23 ##| ##24: napply eqbit_to_eq24
+ ##| ##25: napply eqbit_to_eq25 ##| ##26: napply eqbit_to_eq26
+ ##| ##27: napply eqbit_to_eq27 ##| ##28: napply eqbit_to_eq28
+ ##| ##29: napply eqbit_to_eq29 ##| ##30: napply eqbit_to_eq30
+ ##| ##31: napply eqbit_to_eq31 ##| ##32: napply eqbit_to_eq32
+ ##]
+nqed.
 
 nlemma neq_to_neqbit : ∀n1,n2.n1 ≠ n2 → eq_bit n1 n2 = false.
  #n1; #n2; #H;