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[Merged by Bors] - feat(Sym2/Order): s.inf = t.inf ∧ s.sup = t.sup ↔ s = t #24005

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[Merged by Bors] - feat(Sym2/Order): s.inf = t.inf ∧ s.sup = t.sup ↔ s = t #24005

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b080756
feat(Sym2/Order): Add eq_iff_inf_sup_eq
sorrachai Apr 13, 2025
a537d59
feat(Sym2/Order): Add eq_iff_inf_sup_eq
sorrachai Apr 13, 2025
38f467e
feat(Sym2/Order): Add eq_iff_inf_sup_eq
sorrachai Apr 13, 2025
51fb3db
golf
YaelDillies Apr 14, 2025
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9 changes: 9 additions & 0 deletions Mathlib/Data/Sym/Sym2/Order.lean
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Expand Up @@ -42,4 +42,13 @@ def sortEquiv [LinearOrder α] : Sym2 α ≃ { p : α × α // p.1 ≤ p.2 } whe
right_inv := Subtype.rec <| Prod.rec fun x y hxy =>
Subtype.ext <| Prod.ext (by simp [hxy]) (by simp [hxy])

/-- In a linear order, two symmetric squares are equal if and only if
they have the same infimum and supremum. -/
theorem inf_eq_inf_and_sup_eq_sup [LinearOrder α] {s t : Sym2 α} :
s.inf = t.inf ∧ s.sup = t.sup ↔ s = t := by
induction' s with a b
induction' t with c d
obtain hab | hba := le_total a b <;> obtain hcd | hdc := le_total c d <;>
aesop (add unsafe le_antisymm)

end Sym2
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