Theorems · Theorem · group theory
Set.preimage_smul_inv
∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : MulAction α β] (a : α) (t : Set β),
(fun x => a⁻¹ • x) ⁻¹' t = a • t- Cited by
- 8 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Set.preimagestatement · cited by 4,946
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- Set.preimage_smulproof · cited by 15
- toUnitsproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_smulproof · cited by 10
- MeasurableSet.const_smulproof · cited by 2
- IsCompact.locallyCompactSpace_of_mem_nhds_of_groupproof · cited by 2
- MeasureTheory.Measure.domSMul_applyproof · cited by 1
- ErgodicSMul.of_aestabilizerproof · cited by 0
- MeasureTheory.eventuallyConst_smul_set_aeproof · cited by 0
- MeasureTheory.smulInvariantMeasure_tfaeproof · cited by 0