Theorems · Theorem · order theory
Set.Nonempty.image_const
∀ {α : Type u_1} {β : Type u_2} {s : Set α}, s.Nonempty → ∀ (a : β), (fun x => a) '' s = {a}- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 5,609
- Set.Nonemptystatement and proof · cited by 2,627
- Set.extproof · cited by 2,266
- Set.mem_singletonproof · cited by 183
- Set.eq_of_mem_singletonproof · cited by 22
Cited by26
Results whose statement or proof uses this declaration.
- Set.zero_smul_setproof · cited by 20
- Finset.image_constproof · cited by 5
- isClosedMap_constproof · cited by 4
- wbtw_self_iffproof · cited by 4
- wbtw_iff_left_eq_or_right_mem_image_Iciproof · cited by 4
- Topology.RelCWComplex.closedCell_zero_eq_singletonproof · cited by 4
- Topology.RelCWComplex.openCell_zero_eq_singletonproof · cited by 3
- Set.image_mul_const_uIccproof · cited by 3
- spectrum.map_polynomial_aeval_of_nonemptyproof · cited by 2
- CFC.spectrum_algebraMap_eqproof · cited by 2
- IsLUB.mul_leftproof · cited by 2