Theorems · Theorem · group theory
inv_smul_smul
∀ {G : Type u_3} {α : Type u_5} [inst : Group G] [inst_1 : MulAction G α] (g : G) (a : α), g⁻¹ • g • a = a- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 76 results in Mathlib
- Foundations
- Depth 8 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
- inv_mul_cancelproof · cited by 107
Cited by77
Results whose statement or proof uses this declaration.
- inv_smul_smul₀proof · cited by 80
- MulAction.toPermproof · cited by 30
- inv_smul_eq_iffproof · cited by 16
- eq_inv_smul_iffproof · cited by 12
- tendsto_const_smul_iffproof · cited by 5
- invOf_smul_smulproof · cited by 5
- IsClosed.smul_left_of_isCompactproof · cited by 5
- smul_eq_zero_iff_eqproof · cited by 4
- MulAction.quotient_preimage_image_eq_union_mulproof · cited by 3
- isCusp_SL2Z_iffproof · cited by 3
- MulAction.orbit_smulproof · cited by 3
- Ideal.mem_pointwise_smul_iff_inv_smul_memproof · cited by 3