[Merged by Bors] - feat(data/set/intervals): define set.ord_connected
#3647
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A set `s : set α`, `[preorder α]` is `ord_connected` if for any `x y ∈ s` we have `[x, y] ⊆ s`. For real numbers this property is equivalent to each of the properties `convex s` and `is_preconnected s`. We define it for any `preorder`, prove some basic properties, and migrate lemmas like `convex_I??` and `is_preconnected_I??` to this API.
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A set `s : set α`, `[preorder α]` is `ord_connected` if for any `x y ∈ s` we have `[x, y] ⊆ s`. For real numbers this property is equivalent to each of the properties `convex s` and `is_preconnected s`. We define it for any `preorder`, prove some basic properties, and migrate lemmas like `convex_I??` and `is_preconnected_I??` to this API. Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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A set `s : set α`, `[preorder α]` is `ord_connected` if for any `x y ∈ s` we have `[x, y] ⊆ s`. For real numbers this property is equivalent to each of the properties `convex s` and `is_preconnected s`. We define it for any `preorder`, prove some basic properties, and migrate lemmas like `convex_I??` and `is_preconnected_I??` to this API. Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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A set
s : set α,[preorder α]isord_connectedif forany
x y ∈ swe have[x, y] ⊆ s. For real numbers this propertyis equivalent to each of the properties
convex sand
is_preconnected s. We define it for anypreorder, prove somebasic properties, and migrate lemmas like
convex_I??andis_preconnected_I??to this API.Started as a part of #3640