X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_assembly%2Fnum%2Fquatern_lemmas.ma;h=c2c8a33998be710b0b0d4379f06a0c9dc4b3bc11;hb=11f0f9739cdec05a1058e3492968ecead0be48f0;hp=339d4f701484e529cf85a24927c921e4bc319e62;hpb=601baed778a190b580982b588ebe49ba3f762b30;p=helm.git

diff --git a/helm/software/matita/contribs/ng_assembly/num/quatern_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/quatern_lemmas.ma
index 339d4f701..c2c8a3399 100755
--- a/helm/software/matita/contribs/ng_assembly/num/quatern_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/quatern_lemmas.ma
@@ -39,63 +39,53 @@ ndefinition quatern_destruct : quatern_destruct_aux.
  napply (λx.x).
 nqed.
 
-nlemma symmetric_eqqu : symmetricT quatern bool eq_qu.
- #n1; #n2;
- nelim n1;
+nlemma eq_to_eqqu : ∀n1,n2.n1 = n2 → eq_qu n1 n2 = true.
+ #n1; #n2; #H;
+ nrewrite > H;
  nelim n2;
  nnormalize;
  napply refl_eq.
 nqed.
 
-nlemma eqqu_to_eq : ∀n1,n2.eq_qu n1 n2 = true → n1 = n2.
- #n1; #n2;
- ncases n1;
- ncases n2;
- nnormalize;
- ##[ ##1,6,11,16: #H; napply refl_eq
- ##| ##*: #H; napply (bool_destruct … H)
+nlemma neqqu_to_neq : ∀n1,n2.eq_qu n1 n2 = false → n1 ≠ n2.
+ #n1; #n2; #H;
+ napply (not_to_not (n1 = n2) (eq_qu n1 n2 = true) …);
+ ##[ ##1: napply (eq_to_eqqu n1 n2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
  ##]
 nqed.
 
-nlemma eq_to_eqqu : ∀n1,n2.n1 = n2 → eq_qu n1 n2 = true.
+nlemma eqqu_to_eq : ∀n1,n2.eq_qu n1 n2 = true → n1 = n2.
  #n1; #n2;
  ncases n1;
  ncases n2;
  nnormalize;
  ##[ ##1,6,11,16: #H; napply refl_eq
- ##| ##*: #H; napply (quatern_destruct … H)
+ ##| ##*: #H; napply (bool_destruct … H)
  ##]
 nqed.
 
-nlemma decidable_qu : ∀x,y:quatern.decidable (x = y).
- #x; #y;
- nnormalize;
- nelim x;
- nelim y;
- ##[ ##1,6,11,16: napply (or2_intro1 (? = ?) (? ≠ ?) …); napply refl_eq
- ##| ##*: napply (or2_intro2 (? = ?) (? ≠ ?) …);
-          nnormalize; #H;
-          napply False_ind;
-          napply (quatern_destruct … H)
- ##]
+nlemma neq_to_neqqu : ∀n1,n2.n1 ≠ n2 → eq_qu n1 n2 = false.
+ #n1; #n2; #H;
+ napply (neqtrue_to_eqfalse (eq_qu n1 n2));
+ napply (not_to_not (eq_qu n1 n2 = true) (n1 = n2) ? H);
+ napply (eqqu_to_eq n1 n2).
 nqed.
 
-nlemma neqqu_to_neq : ∀n1,n2.eq_qu n1 n2 = false → n1 ≠ n2.
- #n1; #n2;
- ncases n1;
- ncases n2;
- nnormalize;
- ##[ ##1,6,11,16: #H; napply (bool_destruct … H)
- ##| ##*: #H; #H1; napply (quatern_destruct … H1)
+nlemma decidable_qu : ∀x,y:quatern.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_qu x y = true) (eq_qu x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqqu_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqqu_to_neq … H))
  ##]
 nqed.
 
-nlemma neq_to_neqqu : ∀n1,n2.n1 ≠ n2 → eq_qu n1 n2 = false.
+nlemma symmetric_eqqu : symmetricT quatern bool eq_qu.
  #n1; #n2;
- ncases n1;
- ncases n2;
- nnormalize;
- ##[ ##1,6,11,16: #H; nelim (H (refl_eq …))
- ##| ##*: #H; napply refl_eq
+ napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_qu n1 n2));
+ ##[ ##1: #H; nrewrite > H; napply refl_eq
+ ##| ##2: #H; nrewrite > (neq_to_neqqu n1 n2 H);
+          napply (symmetric_eq ? (eq_qu n2 n1) false);
+          napply (neq_to_neqqu n2 n1 (symmetric_neq ? n1 n2 H))
  ##]
 nqed.