Theorems · Theorem · group theory
smul_eq_iff_eq_inv_smul
∀ {α : Type u_5} {β : Type u_6} [inst : Group α] [inst_1 : MulAction α β] (g : α) {x y : β}, g • x = y ↔ x = g⁻¹ • y- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- MulActionstatement and proof · cited by 1,294
- eq_inv_smul_iffproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_interproof · cited by 2
- Finset.smul_finset_eq_univproof · cited by 1
- Monoid.PushoutI.NormalWord.ext_smulproof · cited by 1
- MulAction.IsBlock.of_subsetproof · cited by 1
- isCancelSMul_iff_eq_one_of_smul_eqproof · cited by 1
- smul_eq_iff_eq_invOf_smulproof · cited by 1
- MulAction.period_invproof · cited by 0
- MulAction.smul_fixedByproof · cited by 0
- Set.smul_set_eq_univproof · cited by 0