Theorems · Theorem · group theory
Set.preimage_smul
∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : MulAction α β] (a : α) (t : Set β),
(fun x => a • x) ⁻¹' t = a⁻¹ • t- Cited by
- 15 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- 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
- MulAction.toPermproof · cited by 30
- Equiv.image_symm_eq_preimageproof · cited by 17
Cited by15
Results whose statement or proof uses this declaration.
- Set.preimage_smul_invproof · cited by 8
- Set.preimage_smul_inv₀proof · cited by 6
- Metric.preimage_smul_closedEBallproof · cited by 3
- Metric.preimage_smul_eballproof · cited by 3
- Metric.preimage_smul_ballproof · cited by 2
- Metric.preimage_smul_closedBallproof · cited by 2
- aeconst_of_dense_aestabilizer_smulproof · cited by 1
- ergodic_smul_of_denseRange_zpowproof · cited by 1
- MeasureTheory.smul_aeproof · cited by 1
- MeasureTheory.aeconst_of_forall_smul_ae_eqproof · cited by 1
- DenseRange.zpow_of_ergodic_mul_leftproof · cited by 1
- Set.preimage_smul₀proof · cited by 0