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≫〉.
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≫〉.