Theorems · Theorem · order theory
Subtype.coe_preimage_self
∀ {α : Type u_1} (s : Set α), Subtype.val ⁻¹' s = Set.univ- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 25 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.preimagestatement and proof · cited by 4,946
- Set.univstatement · cited by 3,945
- Subtype.range_coeproof · cited by 98
- Set.preimage_rangeproof · cited by 38
Cited by46
Results whose statement or proof uses this declaration.
- IsCompact.elim_finite_subcover_imageproof · cited by 8
- connectedComponentIn_subsetproof · cited by 7
- MvPolynomial.mem_supportedproof · cited by 4
- Set.Infinite.exists_subset_card_eqproof · cited by 4
- TopologicalSpace.Opens.IsBasis.exists_finite_of_isCompactproof · cited by 3
- isCompact_setOfPred_finiteMeasure_le_of_isCompactproof · cited by 2
- loc_compact_Haus_tot_disc_of_zero_dimproof · cited by 2
- linearIndepOn_iff'proof · cited by 2
- eq_affineCombination_of_mem_affineSpan_imageproof · cited by 2
- IsCoveringMapOn.isCoveringMap_restrictPreimageproof · cited by 2
- CompleteLattice.isCompactElement_iff_exists_le_iSup_of_le_iSupproof · cited by 1