Theorems · Theorem · group theory
smul_inv
∀ {G : Type u_3} {H : Type u_4} [inst : Group G] [inst_1 : Group H] [inst_2 : MulAction G H] [SMulCommClass G H H]
[IsScalarTower G H H] (g : G) (a : H), (g • a)⁻¹ = g⁻¹ • a⁻¹- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
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.
- Groupstatement and proof · cited by 6,238
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- one_smulproof · cited by 1,374
- MulActionstatement and proof · cited by 1,294
- mul_inv_cancelproof · cited by 128
- inv_eq_of_mul_eq_one_rightproof · cited by 15
- smul_mul_smul_commproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- smul_zpowproof · cited by 0