Theorems · Theorem · order theory
Set.preimage_const_of_mem
∀ {α : Type u_1} {β : Type u_2} {b : β} {s : Set β}, b ∈ s → (fun x => b) ⁻¹' s = Set.univ- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Set.preimagestatement · cited by 4,946
- Set.univstatement · cited by 3,945
- Set.eq_univ_of_forallproof · cited by 80
Cited by14
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.inductionproof · cited by 14
- Ordinal.div_zeroproof · cited by 7
- MeasureTheory.SimpleFunc.const_lintegralproof · cited by 2
- MeasureTheory.SimpleFunc.induction'proof · cited by 1
- MeasureTheory.SimpleFunc.setToSimpleFunc_const'proof · cited by 1
- MeasureTheory.SimpleFunc.setToSimpleFunc_indicatorproof · cited by 1
- MeasurableSpace.comap_constproof · cited by 1
- tendsto_iteproof · cited by 1
- summable_const_iffproof · cited by 1
- Filter.map_constproof · cited by 1
- isProperMap_const_iffproof · cited by 1
- SeminormFamily.basisSets_smul_leftproof · cited by 0