Theorems · Definition
Set.image
{α : Type u} → {β : Type v} → (α → β) → Set α → Set βThe image of s : Set α by f : α → β, written f '' s, is the set of b : β such that
f a = b for some a ∈ s.
- Defined in
- Mathlib.Data.Set.Defs
- Cited by
- 5,609 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 11 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.ofPredproof · cited by 6,101
Cited by5,892
Results whose statement or proof uses this declaration.
- Ideal.mapproof · cited by 692
- Submodule.mapproof · cited by 614
- Set.smulSetproof · cited by 608
- Set.image_congrstatement · cited by 533
- Set.vaddSetproof · cited by 403
- Set.mem_image_of_memstatement · cited by 371
- Set.image_univstatement · cited by 322
- Subgroup.mapproof · cited by 301
- nhdsSetproof · cited by 267
- IsOpenMapproof · cited by 253
- Set.range_compstatement · cited by 223
- Finset.coe_imagestatement · cited by 222
Showing the 200 most cited of 5,892.