Theorems · Theorem · order theory

image_antitone_setOfPred_maximal

∀ {α : Type u_2} {β : Type u_3} {P : α → Prop} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
  (∀ ⦃y x : α⦄, P y → P x → (f y ≤ f x ↔ x ≤ y)) →
    f '' {x | Maximal P x} = {x | Minimal (fun x => ∃ x₀, P x₀ ∧ f x₀ = x) x}

Defined in

Mathlib.Order.Minimal

Cited by

3 results in Mathlib

Foundations

Depth 11 from the axioms · uses propext, Quot.sound

Assumes

PreorderPreorder