feat: Set.ReflOn, Set.SymmOn - #663
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fmontesi
approved these changes
Jun 19, 2026
| /-- `RightQuasiRefl r` is true when a relation `r` is reflexive on its codomain. -/ | ||
| abbrev RightQuasiRefl (r : α → α → Prop) := (cod r).ReflOn r | ||
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| /-- `SymmOn s r` ts true when a relation `r` is symmetric on its restriction to a set `s`. -/ |
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ts -> is.
Rest looks good to me.
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Thanks. I'll wait a bit to merge in case there's any comments on Zulip.
thomaskwaring
approved these changes
Jun 21, 2026
| @[simp, grind =] lemma mem_cod : b ∈ cod r ↔ ∃ a, r a b := .rfl | ||
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| theorem of_dom (hab : r a b) : a ∈ dom r := by grind | ||
| theorem of_cod (hab : r a b) : b ∈ cod r := by grind |
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this naming is a little confusing to me — doesn't the convention usually read "of_{hypothesis}" where here it's "of_{conclusion}" — otherwise lgtm :)
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A first pass at adding definitions corresponding to the concept of having some property of a (homogeneous) relation over a set restriction, as discussed in this thread. I also add lemmas
of_{cod,dom}for convenience of working in the "constructive" case where we explicitly are given the relation as evidence of the (co)domain.