Theorems · Theorem · order theory

Relation.fibration_iff_image_Iic

∀ {α : Type u_1} {β : Type u_2} {f : α → β} [inst : Preorder α] [inst_1 : Preorder β],
  Monotone f →
    (Relation.Fibration (fun x1 x2 => x1 ≤ x2) (fun x1 x2 => x1 ≤ x2) f ↔ ∀ (x : α), f '' Set.Iic x = Set.Iic (f x))

Defined in

Mathlib.Order.UpperLower.Fibration

Cited by

2 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderPreorder