Theorems · Theorem · order theory
Set.kernImage_eq_compl
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s : Set α}, Set.kernImage f s = (f '' sᶜ)ᶜ- Defined in
- Mathlib.Data.Set.Lattice.Image
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.preimageproof · cited by 4,946
- Compl.complstatement · cited by 2,925
- compl_complproof · cited by 229
- Set.preimage_complproof · cited by 43
- Set.kernImagestatement · cited by 21
- Set.image_preimageproof · cited by 16
- GaloisConnection.u_uniqueproof · cited by 3
- Set.preimage_kernImageproof · cited by 2
- GaloisConnection.complproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- Filter.mem_comap_iff_complproof · cited by 3
- Set.kernImage_union_preimageproof · cited by 1
- isClosedMap_iff_kernImageproof · cited by 1
- isOpenMap_iff_kernImageproof · cited by 1
- Set.kernImage_complproof · cited by 1
- Set.kernImage_emptyproof · cited by 1
- Set.kernImage_preimage_eq_iffproof · cited by 0
- isClosedMap_iff_kernImage_interiorproof · cited by 0
- isOpenMap_iff_closure_kernImageproof · cited by 0