mathlib
78655b6e - feat(data/set/intervals): define `set.ord_connected` (#3647)

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5 years ago
feat(data/set/intervals): define `set.ord_connected` (#3647) 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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