X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fdama%2Fdama%2Fbishop_set.ma;h=9fee3d9fd3c0cdd3e640ee9054a84b89bf4d59ce;hb=7e33e23e18dc5d008b3b3dc0052aa4d7b236415e;hp=78176d776816c85c513348d356568924e90c77f0;hpb=3c1ca5620048ad842144fba291f8bc5f0dca7061;p=helm.git

diff --git a/helm/software/matita/contribs/dama/dama/bishop_set.ma b/helm/software/matita/contribs/dama/dama/bishop_set.ma
index 78176d776..9fee3d9fd 100644
--- a/helm/software/matita/contribs/dama/dama/bishop_set.ma
+++ b/helm/software/matita/contribs/dama/dama/bishop_set.ma
@@ -26,7 +26,7 @@ record bishop_set: Type ≝ {
 notation "hvbox(a break # b)" non associative with precedence 45 
   for @{ 'apart $a $b}.
   
-interpretation "bishop_setapartness" 'apart x y = (bs_apart _ x y).
+interpretation "bishop set apartness" 'apart x y = (bs_apart _ x y).
 
 definition bishop_set_of_ordered_set: ordered_set → bishop_set.
 intros (E); apply (mk_bishop_set E (λa,b:E. a ≰ b ∨ b ≰ a));  
@@ -94,3 +94,22 @@ theorem lt_to_excess: ∀E:ordered_set.∀a,b:E. (a < b) → (b ≰ a).
 intros (E a b Lab); cases Lab (LEab Aab); cases Aab (H H);[cases (LEab H)]
 assumption;
 qed.
+
+definition bs_subset ≝ λO:bishop_set.λP,Q:O→Prop.∀x:O.P x → Q x.
+
+interpretation "bishop set subset" 'subset a b = (bs_subset _ a b). 
+
+definition square_bishop_set : bishop_set → bishop_set.
+intro S; apply (mk_bishop_set (S × S));
+[1: intros (x y); apply ((fst x # fst y) ∨ (snd x # snd y));
+|2: intro x; simplify; intro; cases H (X X); clear H; apply (bs_coreflexive ?? X);   
+|3: intros 2 (x y); simplify; intro H; cases H (X X); clear H; [left|right] apply (bs_symmetric ??? X); 
+|4: intros 3 (x y z); simplify; intro H; cases H (X X); clear H;
+    [1: cases (bs_cotransitive ??? (fst z) X); [left;left|right;left]assumption;
+    |2: cases (bs_cotransitive ??? (snd z) X); [left;right|right;right]assumption;]]
+qed.
+
+notation "s 2 \atop \neq" non associative with precedence 90
+  for @{ 'square_bs $s }.
+interpretation "bishop set square" 'square x = (square_bishop_set x).
+interpretation "bishop set square" 'square_bs x = (square_bishop_set x).
\ No newline at end of file