Theorems · Theorem · order theory
Set.range_nonempty
∀ {α : Type u_1} {ι : Sort u_4} [h : Nonempty ι] (f : ι → α), (Set.range f).Nonempty- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 84 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement · cited by 4,705
- Set.Nonemptystatement · cited by 2,627
- Set.range_nonempty_iff_nonemptyproof · cited by 7
Cited by84
Results whose statement or proof uses this declaration.
- ciSup_leproof · cited by 56
- tendsto_atTop_ciSupproof · cited by 13
- isLUB_ciSupproof · cited by 10
- ciSup_eq_of_forall_le_of_forall_lt_exists_gtproof · cited by 8
- Order.IsNormal.map_iSupproof · cited by 8
- exists_eq_ciSup_of_finiteproof · cited by 8
- AddAction.nonempty_orbitproof · cited by 5
- exists_eq_ciSup_of_not_isSuccLimitproof · cited by 5
- ciInf_memproof · cited by 5
- exists_lt_of_lt_ciSupproof · cited by 4
- ENat.exists_eq_iInfproof · cited by 4
- MulAction.nonempty_orbitproof · cited by 4