∀O:ordered_uniform_space.∀l,r:O.
∀U:{[l,r]} square → Prop.∀u:O square → Prop.
restriction_agreement ? l r U u →
- restriction_agreement ? l r (inv U) (inv u).
+ restriction_agreement ? l r (\inv U) (\inv u).
intros 9; split; intro;
[1: apply (unrestrict ????? (segment_square_of_ordered_set_square ??? 〈\snd b,\fst b〉 H2 H1) H H3);
|2: apply (restrict ????? (segment_square_of_ordered_set_square ??? 〈\snd b,\fst b〉 H2 H1) H H3);]
∀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).
+*)
lemma ss_of_bs:
∀O:ordered_set.∀u,v:O.
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 segment_ordered_uniform_space:
∀O:ordered_uniform_space.∀u,v:O.ordered_uniform_space.