Theorems · Theorem · group theory
MulAction.toPerm_apply
∀ {α : Type u_5} {β : Type u_6} [inst : Group α] [inst_1 : MulAction α β] (a : α) (x : β),
(MulAction.toPerm a) x = a • x- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- Equivstatement · cited by 8,337
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- MulAction.toPermstatement and proof · cited by 30
Cited by12
Results whose statement or proof uses this declaration.
- HNNExtension.NormalWord.of_smul_eq_smulproof · cited by 4
- alternatingGroup.stabilizer.surjective_toPermproof · cited by 2
- ProperSMul.isCompact_setOfPred_inter_nonemptyproof · cited by 2
- Projectivization.SL_mulAction_kerproof · cited by 1
- smul_eq_self_of_mem_zpowersproof · cited by 1
- Equiv.Perm.stabilizer.surjective_toPermproof · cited by 1
- Set.powersetCard.mulAction_faithfulproof · cited by 1
- MulAction.toPerm_oneproof · cited by 1
- ModularGroup.exists_bound_of_subgroup_invariant_of_isBigOproof · cited by 1
- MeasureTheory.IsFundamentalDomain.smulproof · cited by 0
- Equiv.Perm.OnCycleFactors.mem_ker_toPermHom_iffproof · cited by 0