Release 0.5.9.

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

diff --git a/helm/software/matita/contribs/ng_assembly/num/bool_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/bool_lemmas.ma
index db5214c6d16fd5092ce33a1507b0bfaad9f3c9c1..b7b9096e871706bddcb98a46ce4b85db2221168c 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/num/bool_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/bool_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                                          *)
 (*                                                                        *)
 (* ********************************************************************** *)
 
@@ -26,7 +26,6 @@ include "num/bool.ma".
 (* BOOLEANI *)
 (* ******** *)
 
-(*
 ndefinition bool_destruct_aux ≝
 Πb1,b2:bool.ΠP:Prop.b1 = b2 →
  match eq_bool b1 b2 with [ true ⇒ P → P | false ⇒ P ].
@@ -38,7 +37,6 @@ ndefinition bool_destruct : bool_destruct_aux.
  nnormalize;
  napply (λx.x).
 nqed.
-*)
 
 nlemma symmetric_eqbool : symmetricT bool bool eq_bool.
  #b1; #b2;
@@ -105,7 +103,7 @@ nlemma eqbool_to_eq : ∀b1,b2:bool.(eq_bool b1 b2 = true) → (b1 = b2).
  ncases b2;
  nnormalize;
  ##[ ##1,4: #H; napply refl_eq
- ##| ##*: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##| ##*: #H; napply (bool_destruct … H)
  ##]
 nqed.
 
@@ -115,7 +113,7 @@ nlemma eq_to_eqbool : ∀b1,b2.b1 = b2 → eq_bool b1 b2 = true.
  ncases b2;
  nnormalize;
  ##[ ##1,4: #H; napply refl_eq
- ##| ##*: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##| ##*: #H; napply (bool_destruct … H)
  ##]
 nqed.
 
@@ -128,7 +126,7 @@ nlemma decidable_bool : ∀x,y:bool.decidable (x = y).
  ##| ##*: napply (or2_intro2 (? = ?) (? ≠ ?) …);
           nnormalize; #H;
           napply False_ind;
-          ndestruct (*napply (bool_destruct … H)*)
+          napply (bool_destruct … H)
  ##]
 nqed.
 
@@ -144,8 +142,8 @@ nlemma neqbool_to_neq : ∀b1,b2:bool.(eq_bool b1 b2 = false) → (b1 ≠ b2).
  ncases b1;
  ncases b2;
  nnormalize;
- ##[ ##1,4: #H; ndestruct (*napply (bool_destruct … H)*)
- ##| ##*: #H; #H1; ndestruct (*napply (bool_destruct … H1)*)
+ ##[ ##1,4: #H; napply (bool_destruct … H)
+ ##| ##*: #H; #H1; napply (bool_destruct … H1)
  ##]
 nqed.
 
@@ -161,15 +159,15 @@ nqed.
 
 nlemma eqfalse_to_neqtrue : ∀x.x = false → x ≠ true.
  #x; nelim x;
- ##[ ##1: #H; ndestruct (*napply (bool_destruct … H)*)
- ##| ##2: #H; nnormalize; #H1; ndestruct (*napply (bool_destruct … H1)*)
+ ##[ ##1: #H; napply (bool_destruct … H)
+ ##| ##2: #H; nnormalize; #H1; napply (bool_destruct … H1)
  ##]
 nqed.
 
 nlemma eqtrue_to_neqfalse : ∀x.x = true → x ≠ false.
  #x; nelim x;
- ##[ ##1: #H; nnormalize; #H1; ndestruct (*napply (bool_destruct … H1)*)
- ##| ##2: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##[ ##1: #H; nnormalize; #H1; napply (bool_destruct … H1)
+ ##| ##2: #H; napply (bool_destruct … H)
  ##]
 nqed.
 
@@ -193,7 +191,7 @@ nlemma andb_true_true_l: ∀b1,b2.(b1 ⊗ b2) = true → b1 = true.
  ncases b2;
  nnormalize;
  ##[ ##1,2: #H; napply refl_eq
- ##| ##*: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##| ##*: #H; napply (bool_destruct … H)
  ##]
 nqed.
 
@@ -203,7 +201,7 @@ nlemma andb_true_true_r: ∀b1,b2.(b1 ⊗ b2) = true → b2 = true.
  ncases b2;
  nnormalize;
  ##[ ##1,3: #H; napply refl_eq
- ##| ##*: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##| ##*: #H; napply (bool_destruct … H)
  ##]
 nqed.
 
@@ -214,7 +212,7 @@ nlemma andb_false2
  ncases b1;
  ncases b2;
  nnormalize;
- ##[ ##1: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##[ ##1: #H; napply (bool_destruct … H)
  ##| ##2,4: #H; napply (or2_intro2 … H)
  ##| ##3: #H; napply (or2_intro1 … H)
  ##]
@@ -228,7 +226,7 @@ nlemma andb_false3
  ncases b2;
  ncases b3;
  nnormalize;
- ##[ ##1: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##[ ##1: #H; napply (bool_destruct … H)
  ##| ##5,6,7,8: #H; napply (or3_intro1 … H)
  ##| ##2,4: #H; napply (or3_intro3 … H)
  ##| ##3: #H; napply (or3_intro2 … H)
@@ -244,7 +242,7 @@ nlemma andb_false4
  ncases b3;
  ncases b4;
  nnormalize;
- ##[ ##1: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##[ ##1: #H; napply (bool_destruct … H)
  ##| ##9,10,11,12,13,14,15,16: #H; napply (or4_intro1 … H)
  ##| ##5,6,7,8: #H; napply (or4_intro2 … H)
  ##| ##3,4: #H; napply (or4_intro3 … H)
@@ -262,7 +260,7 @@ nlemma andb_false5
  ncases b4;
  ncases b5;
  nnormalize;
- ##[ ##1: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##[ ##1: #H; napply (bool_destruct … H)
  ##| ##17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32: #H; napply (or5_intro1 … H)
  ##| ##9,10,11,12,13,14,15,16: #H; napply (or5_intro2 … H)
  ##| ##5,6,7,8: #H; napply (or5_intro3 … H)
@@ -309,7 +307,7 @@ nlemma orb_false_false_l : ∀b1,b2:bool.(b1 ⊕ b2) = false → b1 = false.
  ncases b2;
  nnormalize;
  ##[ ##4: #H; napply refl_eq
- ##| ##*: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##| ##*: #H; napply (bool_destruct … H)
  ##]
 nqed.
 
@@ -319,6 +317,6 @@ nlemma orb_false_false_r : ∀b1,b2:bool.(b1 ⊕ b2) = false → b2 = false.
  ncases b2;
  nnormalize;
  ##[ ##4: #H; napply refl_eq
- ##| ##*: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##| ##*: #H; napply (bool_destruct … H)
  ##]
 nqed.