- λO:ordered_set.λu,v:O.λb:{[u,v]} square.〈fst(fst b),fst(snd b)〉.
+ λO:ordered_set.λu,v:O.λb:{[u,v]} square.〈fst(fst b),fst(snd b)〉.
+
+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".
+alias symbol "pair" (instance 4) = "dependent pair".
+alias symbol "pair" (instance 2) = "dependent pair".
+lemma ss_of_bs:
+ ∀O:ordered_set.∀u,v:O.
+ ∀b:O square.fst b ∈ [u,v] → snd b ∈ [u,v] → {[u,v]} square ≝
+ λO:ordered_set.λu,v:O.
+ λb:(O:bishop_set) square.λH1,H2.〈〈fst b,H1〉,〈snd b,H2〉〉.