∀O:ordered_set.∀u,v:O.{[u,v]} square → (bishop_set_of_ordered_set O) square ≝
λO:ordered_set.λu,v:O.λb:{[u,v]} square.〈fst(fst b),fst(snd b)〉.
-notation < "x \sub \neq" left associative with precedence 91 for @{'bsss $x}.
+notation < "x \sub \neq" with precedence 91 for @{'bsss $x}.
interpretation "bs_of_ss" 'bsss x = (bs_of_ss _ _ _ x).
alias symbol "square" (instance 7) = "ordered set square".
λO:ordered_set.λu,v:O.
λb:(O:bishop_set) square.λH1,H2.〈〈fst b,H1〉,〈snd b,H2〉〉.
-notation < "x \sub \nleq" left associative with precedence 91 for @{'ssbs $x}.
+notation < "x \sub \nleq" with precedence 91 for @{'ssbs $x}.
interpretation "ss_of_bs" 'ssbs x = (ss_of_bs _ _ _ x _ _).
lemma segment_ordered_uniform_space: