Theorems · Theorem · order theory

StrictAnti.mem_upperBounds_image

∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : Preorder β] {f : α → β} {a : α} {s : Set α},
  StrictAnti f → (f a ∈ upperBounds (f '' s) ↔ a ∈ lowerBounds s)

Defined in

Mathlib.Order.Bounds.Image

Cited by

1 results in Mathlib

Foundations

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

Assumes

LinearOrderPreorder