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[Merged by Bors] - feat(CategoryTheory/Category/Preorder): isIso_homOfLE #33877

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[Merged by Bors] - feat(CategoryTheory/Category/Preorder): isIso_homOfLE #33877

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feat(CategoryTheory/Category/Preorder): isIso_homOfLE
joelriou Jan 12, 2026
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joelriou Jan 12, 2026
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removed homOfLE'
joelriou Jan 12, 2026
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Merge remote-tracking branch 'origin/master' into spectral-3-category…
joelriou Jan 16, 2026
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6 changes: 6 additions & 0 deletions Mathlib/CategoryTheory/Category/Preorder.lean
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Expand Up @@ -92,6 +92,12 @@ lemma homOfLE_isIso_of_eq {x y : X} (h : x ≤ y) (heq : x = y) :
IsIso (homOfLE h) :=
⟨homOfLE (le_of_eq heq.symm), by simp⟩

lemma isIso_homOfLE {x y : X} (h : x = y) :
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@vihdzp vihdzp Jan 12, 2026

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This can be weakened to AntisymmRel (· ≤ ·) x y, right?

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@joelriou joelriou Jan 12, 2026

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This would require an extra import. Anyway, the more useful basic lemma would still be the one using an equality as an assumption.

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@vihdzp vihdzp Jan 12, 2026

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If AntisymmRel is a heavy import by any measure, then we should refactor the file!

IsIso (homOfLE (by rw [h]) : x ⟶ y) := by
subst h
change IsIso (𝟙 _)
infer_instance

@[simp, reassoc]
lemma homOfLE_comp_eqToHom {a b c : X} (hab : a ≤ b) (hbc : b = c) :
homOfLE hab ≫ eqToHom hbc = homOfLE (hab.trans (le_of_eq hbc)) :=
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