Theorems · Theorem · order theory
Set.range_inclusion
∀ {α : Type u_1} {s t : Set α} (h : s ⊆ t), Set.range (Set.inclusion h) = {x | ↑x ∈ s}- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 9 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.Elemstatement and proof · cited by 7,166
- Set.ofPredstatement · cited by 6,101
- Set.rangestatement · cited by 4,705
- Set.extproof · cited by 2,266
- Set.inclusionstatement · cited by 145
Cited by12
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.isTranscendenceBasis_iff_isAlgebraicproof · cited by 3
- tprod_setElem_eq_tprod_setElem_sdiffproof · cited by 2
- Topology.IsOpenEmbedding.inclusionproof · cited by 2
- Topology.IsClosedEmbedding.inclusionproof · cited by 1
- Subgroup.inclusion_rangeproof · cited by 1
- AddSubgroup.inclusion_rangeproof · cited by 1
- tsum_setElem_eq_tsum_setElem_sdiffproof · cited by 1
- Module.Dual.eq_of_preReflection_mapsTo'proof · cited by 1
- smoothSheafCommRing.isUnit_stalk_iffproof · cited by 1
- IntermediateField.mem_restrictproof · cited by 1
- TopologicalSpace.Opens.isOpenEmbedding_of_leproof · cited by 1
- isLocalHomeomorphOn_iff_isOpenEmbedding_restrictproof · cited by 0