Theorems · Theorem · group theory
smul_inv_smul
∀ {G : Type u_3} {α : Type u_5} [inst : Group G] [inst_1 : MulAction G α] (g : G) (a : α), g • g⁻¹ • a = a- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- one_smulproof · cited by 1,374
- MulActionstatement and proof · cited by 1,294
- smul_smulproof · cited by 360
- mul_inv_cancelproof · cited by 128
Cited by55
Results whose statement or proof uses this declaration.
- smul_inv_smul₀proof · cited by 59
- MulAction.toPermproof · cited by 30
- inv_smul_eq_iffproof · cited by 16
- eq_inv_smul_iffproof · cited by 12
- IsClosed.smul_left_of_isCompactproof · cited by 5
- Representation.coeff_ofMulActionproof · cited by 4
- Subgroup.smul_apply_eq_smul_apply_inv_smulproof · cited by 4
- units_inv_smulproof · cited by 4
- MeasureTheory.measure_preimage_smulproof · cited by 3
- MulAction.smul_orbitproof · cited by 3
- Finset.inv_smul_mem_iffproof · cited by 3
- IsUnit.smul_sub_iff_sub_inv_smulproof · cited by 3