-notation < "x \sub \neq" non associative with precedence 91 for @{'bsss $x}.
-interpretation "bs_of_ss" 'bsss x =
- (cic:/matita/dama/ordered_uniform/bs_of_ss.con _ _ _ x).
+lemma bs2_of_bss2:
+ ∀O:ordered_set.∀u,v:O.(bishop_set_of_ordered_set {[u,v]}) squareB → (bishop_set_of_ordered_set O) squareB ≝
+ λO:ordered_set.λu,v:O.λb:{[u,v]} squareO.〈\fst(\fst b),\fst(\snd b)〉.
+
+coercion bs2_of_bss2 nocomposites.
+
+(*
+notation < "x \sub \neq" with precedence 91 for @{'bsss $x}.
+interpretation "bs_of_ss" 'bsss x = (bs_of_ss _ _ _ x).
+*)
+
+(*
+lemma ss_of_bs:
+ ∀O:ordered_set.∀u,v:O.
+ ∀b:O squareO.\fst b ∈ [u,v] → \snd b ∈ [u,v] → {[u,v]} squareO ≝
+ λO:ordered_set.λu,v:O.
+ λb:O squareB.λH1,H2.〈≪\fst b,H1≫,≪\snd b,H2≫〉.
+*)
+
+(*
+notation < "x \sub \nleq" with precedence 91 for @{'ssbs $x}.
+interpretation "ss_of_bs" 'ssbs x = (ss_of_bs _ _ _ x _ _).
+*)