[Merged by Bors] - feat(data/set/intervals): define set.ord_connected

src/data/set/intervals/ord_connected.lean

@@ -10,9 +10,9 @@ import data.set.lattice
 # Order-connected sets
 
 We say that a set `s : set α` is `ord_connected` if for all `x y ∈ s` it includes the
-interval `[x, y]`. If `α` is a `conditionally_complete_linear_order` with the `order_topology`,
-then this condition is equivalent to `is_preconnected s`. If `α = ℝ`, then this condition is also
-equivalent to `convex s`.
+interval `[x, y]`. If `α` is a `denesly_ordered` `conditionally_complete_linear_order` with
+the `order_topology`, then this condition is equivalent to `is_preconnected s`. If `α = ℝ`, then
+this condition is also equivalent to `convex s`.
 
 In this file we prove that intersection of a family of `ord_connected` sets is `ord_connected` and
 that all standard intervals are `ord_connected`.
@@ -24,9 +24,9 @@ variables {α : Type*} [preorder α] {s t : set α}
 
 /--
 We say that a set `s : set α` is `ord_connected` if for all `x y ∈ s` it includes the
-interval `[x, y]`. If `α` is a `conditionally_complete_linear_order` with the `order_topology`,
-then this condition is equivalent to `is_preconnected s`. If `α = ℝ`, then this condition is also
-equivalent to `convex s`.
+interval `[x, y]`. If `α` is a `denesly_ordered` `conditionally_complete_linear_order` with
+the `order_topology`, then this condition is equivalent to `is_preconnected s`. If `α = ℝ`, then
+this condition is also equivalent to `convex s`.
 -/
 def ord_connected (s : set α) : Prop := ∀ ⦃x⦄ (hx : x ∈ s) ⦃y⦄ (hy : y ∈ s), Icc x y ⊆ s