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[Merged by Bors] - feat(Order/Sublattice): The range of a LatticeHom is a Sublattice #38740

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[Merged by Bors] - feat(Order/Sublattice): The range of a LatticeHom is a Sublattice #38740

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LatticeHom range
Bergschaf Apr 29, 2026
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Bergschaf Apr 29, 2026
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12 changes: 12 additions & 0 deletions Mathlib/Order/Sublattice.lean
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Expand Up @@ -396,4 +396,16 @@ lemma pi_univ_eq_bot {L : ∀ i, Sublattice (π i)} {i : κ} (hL : L i = ⊥) :
pi_univ_eq_bot_iff.2 ⟨i, hL⟩

end Pi

namespace LatticeHom

/--
The range of `LatticeHom` is a sublattice.
-/
def range (f : LatticeHom α β) := (Sublattice.map f ⊤).copy (Set.range f) image_univ.symm

lemma range_coe : (LatticeHom.range f : Set β) = Set.range f := rfl

end LatticeHom

end Sublattice
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