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[helm.git] / helm / software / matita / contribs / dama / dama / property_exhaustivity.ma

diff --git a/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma b/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma
index 9788d4d353c5eea3b6f29d474945f65510f8ace2..deddf88049f5e60a2108942506b67a65bf79bf80 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma
+++ b/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma
@@ -35,11 +35,11 @@ lemma h_segment_preserves_uparrow:
   ∀C:half_ordered_set.∀s:segment C.∀a:sequence (half_segment_ordered_set C s).
    ∀x,h. uparrow C ⌊n,\fst (a n)⌋ x → uparrow (half_segment_ordered_set C s) a ≪x,h≫.
 intros; cases H (Ha Hx); split;
-[ intro n; intro H; apply (Ha n); apply (sx2x ???? H);
+[ intro n; intro H; apply (Ha n); apply rule H;
 | cases Hx; split; 
-  [ intro n; intro H; apply (H1 n);apply (sx2x ???? H); 
-  | intros; cases (H2 (\fst y)); [2: apply (sx2x ???? H3);] 
-    exists [apply w] apply (x2sx ?? (a w) y H4);]]
+  [ intro n; intro H; apply (H1 n);apply rule H; 
+  | intros; cases (H2 (\fst y)); [2: apply rule H3;] 
+    exists [apply w] apply (x2sx_ ?? (a w) y H4);]]
 qed.
 
 notation "'segment_preserves_uparrow'" non associative with precedence 90 for @{'segment_preserves_uparrow}.
@@ -68,8 +68,6 @@ definition exhaustive ≝
      (a is_increasing → a is_upper_located → a is_cauchy) ∧
      (b is_decreasing → b is_lower_located → b is_cauchy).
 
-STOP
-
 lemma h_uparrow_to_in_segment:
   ∀C:half_ordered_set.
    ∀s:segment C.
@@ -80,13 +78,13 @@ lemma h_uparrow_to_in_segment:
 intros (C H a H1 x H2); unfold in H2; cases H2; clear H2;unfold in H3 H4; cases H4; clear H4; unfold in H2;
 cases (wloss_prop C) (W W); apply prove_in_segment; unfold; 
 [ apply (hle_transitive ??? x ? (H2 O)); lapply (H1 O) as K; unfold in K; rewrite <W in K;
-  cases K; unfold in H4 H6; rewrite <W in H6 H4; simplify in H4 H6; assumption;
+  cases K; unfold in H4 H6; apply H4;
 | intro; cases (H5 ? H4); clear H5 H4;lapply(H1 w) as K; unfold in K; rewrite<W in K;
-  cases K; unfold in H5 H4; rewrite<W in H4 H5; simplify in H4 H5; apply (H5 H6);    
+  cases K; unfold in H5 H4; apply H5; apply H6;    
 | apply (hle_transitive ??? x ?  (H2 O)); lapply (H1 0) as K; unfold in K; rewrite <W in K;
-  cases K; unfold in H4 H6; rewrite <W in H4 H6; simplify in H4 H6; assumption;
+  cases K; unfold in H4 H6; apply H6;
 | intro; cases (H5 ? H4); clear H5 H4;lapply(H1 w) as K; unfold in K; rewrite<W in K;
-  cases K; unfold in H5 H4; rewrite<W in H4 H5; simplify in H4 H5; apply (H4 H6);]    
+  cases K; unfold in H5 H4; apply (H4 H6);]    
 qed.
 
 notation "'uparrow_to_in_segment'" non associative with precedence 90 for @{'uparrow_to_in_segment}.