X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Farithmetics%2Fgcd.ma;h=1fe651915a8f146f1e2d5ad71103c2dbc5a4fe8b;hb=64a752136a679bcab14a9cd01823c18b7cc991de;hp=86b0600beb3862e763f257d9f9d624686574f8c4;hpb=53452958508001e7af3090695b619fe92135fb9e;p=helm.git

diff --git a/matita/matita/lib/arithmetics/gcd.ma b/matita/matita/lib/arithmetics/gcd.ma
index 86b0600be..1fe651915 100644
--- a/matita/matita/lib/arithmetics/gcd.ma
+++ b/matita/matita/lib/arithmetics/gcd.ma
@@ -54,7 +54,7 @@ qed.
 
 lemma divides_to_gcd_aux: ∀p,m,n. O < p → O < n →n ∣ m → 
   gcd_aux p m n = n.
-#p #m #n #posp @(lt_O_n_elim … posp) #l #posn #divnm normalize 
+#p #m #n #posp @(lt_O_n_elim … posp) #l #posn #divnm whd in ⊢ (??%?);
 >divides_to_dividesb_true normalize //
 qed.
 
@@ -69,7 +69,7 @@ qed.
 
 lemma not_divides_to_gcd_aux: ∀p,m,n. 0 < n → n ∤ m → 
   gcd_aux (S p) m n = gcd_aux p n (m \mod n).
-#p #m #n #lenm #divnm normalize >not_divides_to_dividesb_false
+#p #m #n #lenm #divnm whd in ⊢ (??%?); >not_divides_to_dividesb_false
 normalize // qed.
 
 theorem divides_gcd_aux_mn: ∀p,m,n. O < n → n ≤ m → n ≤ p →
@@ -157,8 +157,8 @@ qed.
 
 (* a particular case of the previous theorem, with c=1 *)
 theorem divides_d_gcd: ∀m,n,d. 
- d ∣ m → d ∣ n → d ∣ gcd n m. 
-/2/ (* bello *)
+ d ∣ m → d ∣ n → d ∣ gcd n m.
+#m #n #d #divdn #divdn applyS (divides_d_times_gcd m n d 1) //
 qed.
 
 theorem eq_minus_gcd_aux: ∀p,m,n.O < n → n ≤ m →  n ≤ p →
@@ -182,15 +182,15 @@ theorem eq_minus_gcd_aux: ∀p,m,n.O < n → n ≤ m →  n ≤ p →
       [(* first case *)
        <H @(ex_intro ?? (b+a*(m / n))) @(ex_intro ?? a) %2
        <commutative_plus >distributive_times_plus_r 
-       >(div_mod m n) in ⊢(? ? (? % ?) ?)
+       >(div_mod m n) in ⊢(? ? (? % ?) ?);
        >associative_times <commutative_plus >distributive_times_plus
-       <minus_minus <commutative_plus <plus_minus //
+       <minus_plus <commutative_plus <plus_minus //
       |(* second case *)
         <H @(ex_intro ?? (b+a*(m / n))) @(ex_intro ?? a) %1
         >distributive_times_plus_r
-        >(div_mod m n) in ⊢ (? ? (? ? %) ?)
+        >(div_mod m n) in ⊢ (? ? (? ? %) ?);
         >distributive_times_plus >associative_times
-        <minus_minus <commutative_plus <plus_minus //
+        <minus_plus <commutative_plus <plus_minus //
       ]
     ]
   ]
@@ -367,7 +367,7 @@ qed.
 theorem gcd_1_to_divides_times_to_divides: ∀p,n,m:nat. O < p →
 gcd p n = 1 → p ∣ (n*m) → p ∣ m.
 #p #m #n #posn #gcd1 * #c #nm
-cases(eq_minus_gcd m p) #a * #b * #H >gcd1 in H #H 
+cases(eq_minus_gcd m p) #a * #b * #H >gcd1 in H; #H 
   [@(quotient ?? (a*n-c*b)) >distributive_times_minus <associative_times 
    <associative_times <nm >(commutative_times m) >commutative_times
    >associative_times <distributive_times_minus //
@@ -398,7 +398,7 @@ qed.
 
 theorem divides_to_divides_times: ∀p,q,n. prime p  → p ∤ q →
  p ∣ n → q ∣ n → p*q ∣ n.
-#p #q #n #primep #notdivpq #divpn * #b #eqn (>eqn in divpn)
+#p #q #n #primep #notdivpq #divpn * #b #eqn >eqn in divpn;
 #divpn cases(divides_times_to_divides ??? primep divpn) #H
   [@False_ind /2/ 
   |cases H #c #eqb @(quotient ?? c) >eqb <associative_times //