Theorems · Theorem · order theory

image_monotone_setOfPred_minimal

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

Defined in

Mathlib.Order.Minimal

Cited by

5 results in Mathlib

Foundations

Depth 8 from the axioms · uses propext, Quot.sound

Assumes

PreorderPreorder