Some qed-

[helm.git] / matita / matita / lib / arithmetics / gcd.ma

diff --git a/matita/matita/lib/arithmetics/gcd.ma b/matita/matita/lib/arithmetics/gcd.ma
index 86b0600beb3862e763f257d9f9d624686574f8c4..1490a626e336db7cc42c65f804e9e3b66b15e078 100644 (file)
--- 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 →
@@ -184,13 +184,13 @@ theorem eq_minus_gcd_aux: ∀p,m,n.O < n → n ≤ m →  n ≤ p →
        <commutative_plus >distributive_times_plus_r 
        >(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 ⊢ (? ? (? ? %) ?)
         >distributive_times_plus >associative_times
-        <minus_minus <commutative_plus <plus_minus //
+        <minus_plus <commutative_plus <plus_minus //
       ]
     ]
   ]