Theorems · Theorem · order theory
Set.range_subset_iff
∀ {α : Type u_1} {ι : Sort u_4} {f : ι → α} {s : Set α}, Set.range f ⊆ s ↔ ∀ (y : ι), f y ∈ s- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 99 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 21 definitions · uses propext, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Set.rangestatement · cited by 4,705
- Set.forall_mem_rangeproof · cited by 135
Cited by99
Results whose statement or proof uses this declaration.
- isClosed_propertyproof · cited by 13
- IntermediateField.adjoin_adjoin_leftproof · cited by 6
- Nat.range_cast_intproof · cited by 6
- MeasureTheory.IsStronglyPredictable.measurable_add_oneproof · cited by 6
- cauchySeq_tendsto_of_isCompleteproof · cited by 5
- UniformSpace.subset_countable_closure_of_almost_dense_setproof · cited by 4
- Algebra.adjoin_algebraMap_image_union_eq_adjoin_adjoinproof · cited by 3
- Nat.nth_mem_of_infiniteproof · cited by 3
- Function.Periodic.image_Iocproof · cited by 3
- IsPathConnected.image'proof · cited by 3
- BddBelow.wellFoundedOn_ltproof · cited by 3
- TopologicalSpace.Compacts.range_mapproof · cited by 2