X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Farithmetics%2Fprimes.ma;h=62c0a0081af5ecadfade0e7b0bbaa1ff4a3b216a;hb=cd2f5b59215ea771ac137b9a7b115a05175f45d5;hp=2e2ef98fbc18a2c113ddac96aa996cc96a2debfb;hpb=38bc223769400d37900d3e18d663eefebe5c1223;p=helm.git

diff --git a/matita/matita/lib/arithmetics/primes.ma b/matita/matita/lib/arithmetics/primes.ma
index 2e2ef98fb..62c0a0081 100644
--- a/matita/matita/lib/arithmetics/primes.ma
+++ b/matita/matita/lib/arithmetics/primes.ma
@@ -247,26 +247,24 @@ qed.
 
 (* smallest factor *)
 definition smallest_factor : nat → nat ≝
-λn:nat. if_then_else ? (leb n 1) n
-  (min n 2 (λm.(eqb (n \mod m) O))).
+λn:nat. if leb n 1 then n else min n 2 (λm.(eqb (n \mod m) O)).
 
 theorem smallest_factor_to_min : ∀n. 1 < n → 
 smallest_factor n = (min n 2 (λm.(eqb (n \mod m) O))).
 #n #lt1n normalize >lt_to_leb_false //
 qed.
 
-(* it works ! 
-theorem example1 : smallest_factor 3 = 3.
+example example1 : smallest_factor 3 = 3.
 normalize //
 qed.
 
-theorem example2: smallest_factor 4 = 2.
+example example2: smallest_factor 4 = 2.
 normalize //
 qed.
 
-theorem example3 : smallest_factor 7 = 7.
+example example3 : smallest_factor 7 = 7.
 normalize //
-qed. *)
+qed. 
 
 theorem le_SO_smallest_factor: ∀n:nat. 
   n ≤ 1 → smallest_factor n = n.
@@ -312,7 +310,7 @@ qed.
 
 theorem prime_smallest_factor_n : ∀n. 1 < n → 
   prime (smallest_factor n).
-#n #lt1n (cut (0<n)) [/2/] #posn % /2/ #m #divmmin #lt1m
+#n #lt1n (cut (0<n)) [/2/] #posn % (* bug? *) [/2/] #m #divmmin #lt1m
 @le_to_le_to_eq
   [@divides_to_le // @lt_O_smallest_factor //
   |>smallest_factor_to_min // @true_to_le_min //
@@ -339,16 +337,16 @@ definition primeb ≝ λn:nat.
   (leb 2 n) ∧ (eqb (smallest_factor n) n).
 
 (* it works! *)
-theorem example4 : primeb 3 = true.
+example example4 : primeb 3 = true.
 normalize // qed.
 
-theorem example5 : primeb 6 = false.
+example example5 : primeb 6 = false.
 normalize // qed.
 
-theorem example6 : primeb 11 = true.
+example example6 : primeb 11 = true.
 normalize // qed.
 
-theorem example7 : primeb 17 = true.
+example example7 : primeb 17 = true.
 normalize // qed.
 
 theorem primeb_true_to_prime : ∀n:nat.
@@ -440,20 +438,20 @@ let rec nth_prime n ≝ match n with
     min upper_bound (S previous_prime) primeb].
 
 lemma nth_primeS: ∀n.nth_prime (S n) = 
-  let previous_prime ≝ nth_prime n in
+   (let previous_prime ≝ nth_prime n in
     let upper_bound ≝ S previous_prime! in
-    min upper_bound (S previous_prime) primeb.
+    min upper_bound (S previous_prime) primeb).
 // qed.
     
 (* it works *)
-theorem example11 : nth_prime 2 = 5.
+example example11 : nth_prime 2 = 5.
 normalize // qed.
 
-theorem example12: nth_prime 3 = 7.
+example example12: nth_prime 3 = 7.
 normalize //
 qed.
 
-theorem example13 : nth_prime 4 = 11.
+example example13 : nth_prime 4 = 11.
 normalize // qed.
 
 (* done in 13.1369330883s -- qualcosa non va: // lentissimo 
@@ -481,7 +479,7 @@ change with
 (let previous_prime ≝ (nth_prime n) in
  let upper_bound ≝ S previous_prime! in
  S previous_prime ≤ min upper_bound (S previous_prime) primeb)
-apply le_min_l
+@le_min_l
 qed.
 
 theorem lt_SO_nth_prime_n : ∀n:nat. 1 < nth_prime n.