Theorems · Theorem · order theory
Set.monotone_image
∀ {α : Type u_1} {β : Type u_2} {f : α → β}, Monotone (Set.image f)Set.image is monotone. See Set.image_mono for the statement in terms of ⊆.
- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.imagestatement · cited by 5,609
- Monotonestatement · cited by 1,397
- Set.image_monoproof · cited by 197
Cited by9
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_mapproof · cited by 5
- FreeCommRing.isSupported_upwardsproof · cited by 1
- Ideal.spanNorm_monoproof · cited by 1
- Ideal.spanNorm_mul_spanNorm_leproof · cited by 1
- cantorSet_eq_union_halvesproof · cited by 1
- uniform_extend_subtypeproof · cited by 0
- AddCircle.addWellApproximable_ae_empty_or_univproof · cited by 0
- Function.Injective.image_strictMonoproof · cited by 0