Theorems · Theorem · order theory
MonotoneOn.map_isGreatest
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β} {t : Set α} {a : α},
MonotoneOn f t → IsGreatest t a → IsGreatest (f '' t) (f a)A monotone map sends a greatest element of a set to a greatest element of its image.
- Defined in
- Mathlib.Order.Bounds.Image
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement · cited by 5,609
- Set.mem_image_of_memproof · cited by 371
- MonotoneOnstatement and proof · cited by 311
- IsGreateststatement and proof · cited by 112
- MonotoneOn.mem_upperBounds_image_selfproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Unitary.norm_sub_one_sq_eqproof · cited by 2
- MonotoneOn.exists_monotone_extensionproof · cited by 2
- MonotoneOn.nnnorm_cfcₙproof · cited by 1
- AntitoneOn.map_isGreatestproof · cited by 0
- MonotoneOn.nnnorm_cfcproof · cited by 0