done

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

diff --git a/helm/software/matita/contribs/dama/dama/supremum.ma b/helm/software/matita/contribs/dama/dama/supremum.ma
index 7a52e5f064260f1a9f04463a4414e8b0c7b6962a..bad35177b12bd3d2c4601f6eb588f9af999a70d1 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/supremum.ma
+++ b/helm/software/matita/contribs/dama/dama/supremum.ma
@@ -209,10 +209,10 @@ notation "𝕝 \sub term 90 s p" non associative with precedence 45 for @{'low $
  
 definition seg_u ≝
  λO:half_ordered_set.λs:segment O.λP: O → CProp.
-   wloss O ? (λl,u.P u) (seg_l_ ? s) (seg_u_ ? s).
+   wloss O ? (λl,u.P l) (seg_u_ ? s) (seg_l_ ? s).
 definition seg_l ≝
  λO:half_ordered_set.λs:segment O.λP: O → CProp.
-   wloss O ? (λl,u.P u) (seg_u_ ? s) (seg_l_ ? s). 
+   wloss O ? (λl,u.P l) (seg_l_ ? s) (seg_u_ ? s). 
  
 interpretation "uppper" 'upp s P = (seg_u (os_l _) s P).
 interpretation "lower" 'low s P = (seg_l (os_l _) s P).
@@ -221,7 +221,7 @@ interpretation "lower dual" 'low s P = (seg_u (os_r _) s P).
  
 definition in_segment ≝ 
   λO:half_ordered_set.λs:segment O.λx:O.
-    wloss O ? (λp1,p2.p1 ∧ p2) (seg_u ? s (λu.u ≤≤ x)) (seg_l ? s (λl.x ≤≤ l)).
+    wloss O ? (λp1,p2.p1 ∧ p2) (seg_l ? s (λl.l ≤≤ x)) (seg_u ? s (λu.x ≤≤ u)).
 
 notation "‡O" non associative with precedence 90 for @{'segment $O}.
 interpretation "Ordered set sergment" 'segment x = (segment x).
@@ -350,26 +350,33 @@ notation "'segment_preserves_infimum'" non associative with precedence 90 for @{
 interpretation "segment_preserves_supremum" 'segment_preserves_supremum = (h_segment_preserves_supremum (os_l _)).
 interpretation "segment_preserves_infimum" 'segment_preserves_infimum = (h_segment_preserves_supremum (os_r _)).
 
-(* TEST, ma quanto godo! *)
-lemma segment_preserves_infimum2:
+(*
+test segment_preserves_infimum2:
   ∀O:ordered_set.∀s:‡O.∀a:sequence {[s]}.∀x:{[s]}. 
     ⌊n,\fst (a n)⌋ is_decreasing ∧ 
     (\fst x) is_infimum ⌊n,\fst (a n)⌋ → a ↓ x.
 intros; apply (segment_preserves_infimum s a x H);
 qed.
 *)
-           
+       
 (* Definition 2.10 *)
+
 alias symbol "pi2" = "pair pi2".
 alias symbol "pi1" = "pair pi1".
+(*
 definition square_segment ≝ 
-  λO:ordered_set.λa,b:O.λx: O squareO.
-    And4 (\fst x ≤ b) (a ≤ \fst x) (\snd x ≤ b) (a ≤ \snd x).
- 
+  λO:half_ordered_set.λs:segment O.λx: square_half_ordered_set O.
+    in_segment ? s (\fst x) ∧ in_segment ? s (\snd x).
+*) 
 definition convex ≝
-  λO:ordered_set.λU:O squareO → Prop.
-    ∀p.U p → \fst p ≤ \snd p → ∀y. 
-      square_segment O (\fst p) (\snd p) y → U y.
+  λO:half_ordered_set.λU:square_half_ordered_set O → Prop.
+    ∀s.U s → le O (\fst s) (\snd s) → 
+     ∀y. 
+       le O (\fst y) (\snd s) → 
+       le O (\fst s) (\fst y) →
+       le O (\snd y) (\snd s) →
+       le O (\fst y) (\snd y) →
+       U y.
   
 (* Definition 2.11 *)  
 definition upper_located ≝
@@ -394,8 +401,8 @@ interpretation "Ordered set lower locatedness" 'lower_located s =
 lemma h_uparrow_upperlocated:
   ∀C:half_ordered_set.∀a:sequence C.∀u:C.uparrow ? a u → upper_located ? a.
 intros (C a u H); cases H (H2 H3); clear H; intros 3 (x y Hxy);
-cases H3 (H4 H5); clear H3; cases (hos_cotransitive ??? u Hxy) (W W);
-[2: cases (H5 ? W) (w Hw); left; exists [apply w] assumption;
+cases H3 (H4 H5); clear H3; cases (hos_cotransitive C y x u Hxy) (W W);
+[2: cases (H5 x W) (w Hw); left; exists [apply w] assumption;
 |1: right; exists [apply u]; split; [apply W|apply H4]]
 qed.