(* *)
(**************************************************************************)
-include "ordered_set.ma".
+include "dama/ordered_set.ma".
(* Definition 2.2, setoid *)
record bishop_set: Type ≝ {
bs_cotransitive: cotransitive ? bs_apart
}.
-interpretation "bishop set apartness" '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));
(* Definition 2.2 (2) *)
definition eq ≝ λA:bishop_set.λa,b:A. ¬ (a # b).
-interpretation "Bishop set alikeness" 'napart a b = (eq _ a b).
+interpretation "Bishop set alikeness" 'napart a b = (eq ? a b).
lemma eq_reflexive:∀E:bishop_set. reflexive ? (eq E).
intros (E); unfold; intros (x); apply bs_coreflexive;
definition bs_subset ≝ λO:bishop_set.λP,Q:O→Prop.∀x:O.P x → Q x.
-interpretation "bishop set subset" 'subseteq a b = (bs_subset _ a b).
+interpretation "bishop set subset" 'subseteq a b = (bs_subset ? a b).
definition square_bishop_set : bishop_set → bishop_set.
intro S; apply (mk_bishop_set (S × S));
notation > "s 'squareB'" non associative with precedence 90
for @{ 'squareB $s }.
interpretation "bishop set square" 'squareB x = (square_bishop_set x).
-interpretation "bishop set square" 'square_bs x = (square_bishop_set x).
\ No newline at end of file
+interpretation "bishop set square" 'square_bs x = (square_bishop_set x).