X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Farithmetics%2Fprimes.ma;h=68e511e982617f293eedfc320aaa6be1ec888447;hb=81fc94f4f091ec35d41e2711207218d255b75273;hp=7c5df29f35151cebe5d3c6664368c8ee9f2ece73;hpb=ddc80515997a3f56085c6234d4db326141e189aa;p=helm.git

diff --git a/matita/matita/lib/arithmetics/primes.ma b/matita/matita/lib/arithmetics/primes.ma
index 7c5df29f3..68e511e98 100644
--- a/matita/matita/lib/arithmetics/primes.ma
+++ b/matita/matita/lib/arithmetics/primes.ma
@@ -247,8 +247,7 @@ 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))).
@@ -439,9 +438,9 @@ 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 *)