Theorems · Theorem · order theory
Subtype.image_preimage_coe
∀ {α : Type u_1} (s t : Set α), Subtype.val '' Subtype.val ⁻¹' t = s ∩ t- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 5,609
- Set.preimagestatement · cited by 4,946
- Subtype.range_coeproof · cited by 98
- Set.image_preimage_eq_range_interproof · cited by 11
Cited by37
Results whose statement or proof uses this declaration.
- Subtype.image_preimage_valproof · cited by 17
- Subgroup.subgroupOf_map_subtypeproof · cited by 10
- MeasureTheory.OuterMeasure.restrict_applyproof · cited by 9
- MeasurableSet.subtype_imageproof · cited by 7
- IsPreconnected.subset_connectedComponentInproof · cited by 6
- AddSubgroup.addSubgroupOf_map_subtypeproof · cited by 5
- MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coeproof · cited by 4
- maximal_orthonormal_iff_orthogonalComplement_eq_botproof · cited by 3
- loc_compact_Haus_tot_disc_of_zero_dimproof · cited by 2
- Topology.IsLocallyConstructible.isConstructible_of_subset_of_isCompactproof · cited by 2
- Subtype.preimage_coe_eq_preimage_coe_iffproof · cited by 2
- Dynamics.coverEntropy_restrict_subsetproof · cited by 2