Theorems · Theorem · group theory
Set.image_add_left
∀ {α : Type u_2} [inst : AddGroup α] {t : Set α} {a : α}, (fun x => a + x) '' t = (fun x => -a + x) ⁻¹' t- Cited by
- 44 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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
- Set.imagestatement · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- AddGroupstatement and proof · cited by 4,410
- neg_add_cancel_leftproof · cited by 84
- add_neg_cancel_leftproof · cited by 76
- Set.image_eq_preimage_of_inverseproof · cited by 27
Cited by44
Results whose statement or proof uses this declaration.
- Valuation.mem_nhds_iffproof · cited by 6
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4
- singleton_add_ballproof · cited by 4
- spectrum.singleton_add_eqproof · cited by 4
- MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smulproof · cited by 3
- MeasureTheory.Measure.addHaar_submoduleproof · cited by 3
- ApproximatesLinearOn.norm_fderiv_sub_leproof · cited by 3
- convexOn_distproof · cited by 2
- Set.image_const_sub_Iioproof · cited by 2
- Set.image_const_sub_Ioiproof · cited by 2
- RootPairing.chainCoeff_chainTopIdx_auxproof · cited by 2
- Disjoint.exists_open_convexesproof · cited by 2