X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_assembly%2Fnum%2Foct_lemmas.ma;h=d6c0145980c93c28c7635ff3c592d61d828a3e6f;hb=f9b16ad62794042c2b31c6e3433b3c4035f8a0d5;hp=7cb82090dac1d0945cd867272545e200bea83d5d;hpb=601baed778a190b580982b588ebe49ba3f762b30;p=helm.git

diff --git a/helm/software/matita/contribs/ng_assembly/num/oct_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/oct_lemmas.ma
index 7cb82090d..d6c014598 100755
--- a/helm/software/matita/contribs/ng_assembly/num/oct_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/oct_lemmas.ma
@@ -39,63 +39,53 @@ ndefinition oct_destruct : oct_destruct_aux.
  napply (λx.x).
 nqed.
 
-nlemma symmetric_eqoct : symmetricT oct bool eq_oct.
- #n1; #n2;
- nelim n1;
+nlemma eq_to_eqoct : ∀n1,n2.n1 = n2 → eq_oct n1 n2 = true.
+ #n1; #n2; #H;
+ nrewrite > H;
  nelim n2;
  nnormalize;
  napply refl_eq.
 nqed.
 
-nlemma eqoct_to_eq : ∀n1,n2.eq_oct n1 n2 = true → n1 = n2.
- #n1; #n2;
- ncases n1;
- ncases n2;
- nnormalize;
- ##[ ##1,10,19,28,37,46,55,64: #H; napply refl_eq
- ##| ##*: #H; napply (bool_destruct … H)
+nlemma neqoct_to_neq : ∀n1,n2.eq_oct n1 n2 = false → n1 ≠ n2.
+ #n1; #n2; #H;
+ napply (not_to_not (n1 = n2) (eq_oct n1 n2 = true) …);
+ ##[ ##1: napply (eq_to_eqoct n1 n2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
  ##]
 nqed.
 
-nlemma eq_to_eqoct : ∀n1,n2.n1 = n2 → eq_oct n1 n2 = true.
+nlemma eqoct_to_eq : ∀n1,n2.eq_oct n1 n2 = true → n1 = n2.
  #n1; #n2;
  ncases n1;
  ncases n2;
  nnormalize;
  ##[ ##1,10,19,28,37,46,55,64: #H; napply refl_eq
- ##| ##*: #H; napply (oct_destruct … H)
+ ##| ##*: #H; napply (bool_destruct … H)
  ##]
 nqed.
 
-nlemma decidable_oct : ∀x,y:oct.decidable (x = y).
- #x; #y;
- nnormalize;
- nelim x;
- nelim y;
- ##[ ##1,10,19,28,37,46,55,64: napply (or2_intro1 (? = ?) (? ≠ ?) …); napply refl_eq
- ##| ##*: napply (or2_intro2 (? = ?) (? ≠ ?) …);
-          nnormalize; #H;
-          napply False_ind;
-          napply (oct_destruct … H)
- ##]
+nlemma neq_to_neqoct : ∀n1,n2.n1 ≠ n2 → eq_oct n1 n2 = false.
+ #n1; #n2; #H;
+ napply (neqtrue_to_eqfalse (eq_oct n1 n2));
+ napply (not_to_not (eq_oct n1 n2 = true) (n1 = n2) ? H);
+ napply (eqoct_to_eq n1 n2).
 nqed.
 
-nlemma neqoct_to_neq : ∀n1,n2.eq_oct n1 n2 = false → n1 ≠ n2.
- #n1; #n2;
- ncases n1;
- ncases n2;
- nnormalize;
- ##[ ##1,10,19,28,37,46,55,64: #H; napply (bool_destruct … H)
- ##| ##*: #H; #H1; napply (oct_destruct … H1)
+nlemma decidable_oct : ∀x,y:oct.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_oct x y = true) (eq_oct x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqoct_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqoct_to_neq … H))
  ##]
 nqed.
 
-nlemma neq_to_neqoct : ∀n1,n2.n1 ≠ n2 → eq_oct n1 n2 = false.
+nlemma symmetric_eqoct : symmetricT oct bool eq_oct.
  #n1; #n2;
- ncases n1;
- ncases n2;
- nnormalize;
- ##[ ##1,10,19,28,37,46,55,64: #H; nelim (H (refl_eq …))
- ##| ##*: #H; napply refl_eq
+ napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_oct n1 n2));
+ ##[ ##1: #H; nrewrite > H; napply refl_eq
+ ##| ##2: #H; nrewrite > (neq_to_neqoct n1 n2 H);
+          napply (symmetric_eq ? (eq_oct n2 n1) false);
+          napply (neq_to_neqoct n2 n1 (symmetric_neq ? n1 n2 H))
  ##]
 nqed.