Theorems · Theorem · group theory
Set.preimage_vadd
∀ {α : Type u_2} {β : Type u_3} [inst : AddGroup α] [inst_1 : AddAction α β] (a : α) (t : Set β),
(fun x => a +ᵥ x) ⁻¹' t = -a +ᵥ t- Cited by
- 14 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.
Cites8
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
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddstatement · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.vaddSetstatement · cited by 403
- AddAction.toPermproof · cited by 21
- Equiv.image_symm_eq_preimageproof · cited by 17
Cited by14
Results whose statement or proof uses this declaration.
- Set.preimage_vadd_negproof · cited by 10
- Metric.preimage_vadd_closedEBallproof · cited by 3
- Metric.preimage_vadd_eballproof · cited by 3
- Set.iUnion_vadd_eq_ofPred_existsproof · cited by 2
- Metric.preimage_vadd_ballproof · cited by 2
- Metric.preimage_vadd_closedBallproof · cited by 2
- aeconst_of_dense_aestabilizer_vaddproof · cited by 1
- MeasureTheory.vadd_aeproof · cited by 1
- MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_leproof · cited by 1
- ergodic_vadd_of_denseRange_zsmulproof · cited by 1
- MeasureTheory.aeconst_of_forall_vadd_ae_eqproof · cited by 1
- DenseRange.zsmul_of_ergodic_add_leftproof · cited by 1