-
-alias symbol "square" (instance 8) = "bishop set square".
-lemma bs_of_ss:
- ∀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" 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〉〉.
-
-notation < "x \sub \nleq" with precedence 91 for @{'ssbs $x}.
-interpretation "ss_of_bs" 'ssbs x = (ss_of_bs _ _ _ x _ _).
+
+lemma bs2_of_bss2:
+ ∀O:ordered_set.∀s:‡O.(bishop_set_of_ordered_set {[s]}) squareB → (bishop_set_of_ordered_set O) squareB ≝
+ λO:ordered_set.λs:‡O.λb:{[s]} squareO.〈\fst(\fst b),\fst(\snd b)〉.
+
+coercion bs2_of_bss2 nocomposites.
+
+(*
+lemma xxx :
+ ∀O,s,x.bs2_of_bss2 (ordered_set_OF_ordered_uniform_space O) s x
+ =
+ x.
+intros; reflexivity;
+*)