Theorems · Theorem · order theory

MonotoneOn.mem_lowerBounds_image

∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β} {s t : Set α} {a : α},
  MonotoneOn f t → s ⊆ t → a ∈ lowerBounds s → a ∈ t → f a ∈ lowerBounds (f '' s)

Defined in

Mathlib.Order.Bounds.Image

Cited by

4 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderPreorder