Theorems · Theorem · order theory

image_latticeClosure

∀ {α : Type u_3} {β : Type u_4} [inst : Lattice α] [inst_1 : Lattice β] (s : Set α) (f : α → β),
  (∀ (a b : α), f (a ⊔ b) = f a ⊔ f b) →
    (∀ (a b : α), f (a ⊓ b) = f a ⊓ f b) → f '' latticeClosure s = latticeClosure (f '' s)

Defined in

Mathlib.Order.SupClosed

Cited by

1 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LatticeLattice