* Almost ready for release 0.99.1.

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

diff --git a/matita/matita/lib/arithmetics/minimization.ma b/matita/matita/lib/arithmetics/minimization.ma
index eda9d016618d1031be5b126b65b35ca105b9ee11..143104c50a75b98371aa59b9225ad86834b40c60 100644 (file)
--- a/matita/matita/lib/arithmetics/minimization.ma
+++ b/matita/matita/lib/arithmetics/minimization.ma
@@ -40,7 +40,7 @@ qed.
 
 theorem lt_max_n : ∀f.∀n. O < n → max n f < n.
 #f #n #posn @(lt_O_n_elim ? posn) #m
-normalize (cases (f m)) normalize apply le_S_S //
+normalize (cases (f m)) normalize @le_S_S //
 @le_max_n qed.
 
 theorem le_to_le_max : ∀f.∀n,m.
@@ -122,7 +122,7 @@ qed.
 theorem max_f_g: ∀f,g,n.(∀i. i < n → f i = g i) → 
   max n f = max n g.
 #f #g #n (elim n) //
-#m #Hind #ext normalize >ext >Hind //
+#m #Hind #ext normalize >ext normalize {Hind} >Hind //
 #i #ltim @ext /2/
 qed.
 
@@ -230,8 +230,8 @@ lemma min_exists: ∀f.∀t,m. m < t → f m = true →
   [#b #lebm #ismin #eqtb @False_ind @(absurd … lebm) <eqtb
    @lt_to_not_le //
   |#d #Hind #b #lebm #ismin #eqt cases(le_to_or_lt_eq …lebm)
-    [#ltbm >false_min /2/ @Hind // 
-      [#i #H #H1 @ismin /2/ | >eqt normalize //]
+    [#ltbm >false_min /2/ @Hind //
+      [#i #H #H1 @ismin /2/ | >eqt normalize //] 
     |#eqbm >true_min //
     ]
   ]