X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Farithmetics%2Fprimes.ma;h=3898105c6aaac49345f32c6ea925e52daf0029ed;hb=1cd2f9aa6e0aee9eb4939b39c985b6ad6605092b;hp=71e372f96722f893ebd3889a0b78eaf59f37d1fb;hpb=7ad16d18416a08382d62747fce4a0ac18ee557e0;p=helm.git

diff --git a/matita/matita/lib/arithmetics/primes.ma b/matita/matita/lib/arithmetics/primes.ma
index 71e372f96..3898105c6 100644
--- a/matita/matita/lib/arithmetics/primes.ma
+++ b/matita/matita/lib/arithmetics/primes.ma
@@ -361,7 +361,7 @@ qed.
 
 theorem primeb_false_to_not_prime : ∀n:nat.
   primeb n = false → ¬ (prime n).
-#n #H cut ((leb 2 n ∧ (eqb (smallest_factor n) n)) = false) [>H //] 
+#n #H cut ((leb 2 n ∧ (eqb (smallest_factor n) n)) = false) [@H] 
 @leb_elim 
   [#_ #H1 @(not_to_not … (prime_to_smallest_factor … ))
    @eqb_false_to_not_eq @H1
@@ -465,7 +465,7 @@ qed.
 theorem prime_nth_prime : ∀n:nat.prime (nth_prime n).
 #n (cases n) 
   [@primeb_true_to_prime //
-  |#m >nth_primeS @primeb_true_to_prime @f_min_true
+  |#m >nth_primeS @primeb_true_to_prime check f_min_true @(f_min_true primeb)
    @(ex_intro nat ? (smallest_factor (S (nth_prime m)!)))
    % [% // @le_S_S @(transitive_le … (le_smallest_factor_n …))
       <plus_n_Sm @le_plus_n_r