Theorems · Theorem · order theory
Set.finite_range
∀ {α : Type u} {ι : Sort w} (f : ι → α) [Finite ι], (Set.range f).Finite- Defined in
- Mathlib.Data.Set.Finite.Range
- Cited by
- 58 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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.
- Set.rangestatement and proof · cited by 4,705
- Finitestatement and proof · cited by 3,029
- Set.Finitestatement · cited by 1,814
- Set.toFiniteproof · cited by 174
Cited by59
Results whose statement or proof uses this declaration.
- Filter.iInter_memproof · cited by 12
- exists_eq_ciSup_of_finiteproof · cited by 8
- Submodule.fg_iff_exists_fin_generating_familyproof · cited by 6
- isOpen_iInter_of_finiteproof · cited by 6
- isCompact_iUnionproof · cited by 6
- Directed.finite_leproof · cited by 5
- Set.finite_subset_iUnionproof · cited by 4
- refinement_of_locallyCompact_sigmaCompact_of_nhds_basis_setproof · cited by 3
- Topology.IsLower.isTopologicalBasisproof · cited by 3
- ConvexOn.locallyLipschitzOnproof · cited by 3
- Module.finitePresentation_of_free_of_surjectiveproof · cited by 3
- IsIntegralClosure.isNoetherianproof · cited by 3