Theorems · Theorem · order theory
Monotone.map_bddAbove
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Monotone f → ∀ {s : Set α}, BddAbove s → BddAbove (f '' s)The image under a monotone function of a set which is bounded above is bounded above. See also
BddAbove.image2.
- Defined in
- Mathlib.Order.Bounds.Image
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, 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 and proof · cited by 5,609
- Monotonestatement and proof · cited by 1,397
- BddAbovestatement and proof · cited by 620
- upperBoundsproof · cited by 263
- Monotone.mem_upperBounds_imageproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- Archimedean.ratLt'_bddAboveproof · cited by 4
- Monotone.tendsto_nhdsLTproof · cited by 4
- BddAbove.range_comp_leftproof · cited by 3
- Monotone.le_csSup_imageproof · cited by 2
- GaloisConnection.bddAbove_l_imageproof · cited by 2
- GaloisConnection.l_csSup_of_directedOn'proof · cited by 2
- Antitone.map_bddAboveproof · cited by 1
- BddAbove.smul_of_nonnegproof · cited by 0
- WithBot.coe_sSup'proof · cited by 0