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[helm.git] / matita / matita / lib / arithmetics / chebyshev / bertrand.ma

diff --git a/matita/matita/lib/arithmetics/chebyshev/bertrand.ma b/matita/matita/lib/arithmetics/chebyshev/bertrand.ma
index 082008d68f88c5714201ebcbe0bf37d2d2566ead..8f41262e3b7519b5bb843605504e5a31c0ebc4e4 100644 (file)
--- a/matita/matita/lib/arithmetics/chebyshev/bertrand.ma
+++ b/matita/matita/lib/arithmetics/chebyshev/bertrand.ma
@@ -166,7 +166,7 @@ elim (log p (2*n))
           [@leb_true_to_le //
           |>commutative_times in ⊢ (??%); > times_exp
            @(transitive_le ? (exp n 2))
-            [<associative_times >exp_2 in ⊢ (??%); @le_times //
+            [<associative_times >exp_2 in ⊢ (??%); @le_times [@le18|//]
             |@(le_exp1 … (lt_O_S ?))
              @(le_plus_to_le 3)
              cut (3+2*n/3*3 = S(2*n/3)*3) [//] #eq1 >eq1
@@ -414,7 +414,7 @@ cut (0<n) [@(lt_to_le_to_lt … len) @lt_O_S] #posn
          <exp_S <plus_minus_m_m [2:@lt_O_log //]
          -Hind #Hind <Hclog @(transitive_le … Hind)
          >(eq_log_exp … (le_n ?)) >(eq_log_exp … (le_n ?))
-         >plus_minus_commutative [2:@lt_O_log //]
+         >plus_minus_associative [2:@lt_O_log //]
          cut (2+3 ≤ 2+log 2 m) 
           [@monotonic_le_plus_r @(le_exp_to_le 2) [@le_n|>Hclog @lt_to_le @lt8m]]
          generalize in match (2+log 2 m); #a #Hle >(commutative_times 2 a)