Mathlib Map

Theorems · Definition · group theory

Equiv.mulLeft

{G : Type u_5} → [Group G] → G → Equiv.Perm G

Left multiplication in a Group is a permutation of the underlying type.

Defined in
Mathlib.Algebra.Group.Units.Equiv
Cited by
19 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
Group
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

OrderIso.mulLeft · cited by 18OrderIso.mulLeftHomeomorph.mulLeft · cited by 14Homeomorph.mulLeftGroup.mulLeft_bijective · cited by 7Group.mulLeft_bijectiveEquiv.mulLeft_symm · cited by 3Equiv.mulLeft_symmAnalyticOn.iteratedFDerivWithin_comp_perm · cited by 3AnalyticOn.iteratedFDeriv…IsometryEquiv.mulLeft · cited by 3IsometryEquiv.mulLeftHomeomorph.shearMulRight · cited by 2Homeomorph.shearMulRightSubgroup.normalCore_eq_iInf_map_conj · cited by 1Subgroup.normalCore_eq_iI…Equiv.inv_mulLeft · cited by 1Equiv.inv_mulLeftMeasurableEquiv.shearMulRight · cited by 1MeasurableEquiv.shearMulR…comap_conj_nhds_one · cited by 1comap_conj_nhds_oneMultilinearMap.domCoprod_alternization · cited by 1MultilinearMap.domCoprod_…OnePoint.IsBoundedAt.smul_iff · cited by 1IsBoundedAt.smul_iffEquiv.pow_mulLeft · cited by 1Equiv.pow_mulLeftOnePoint.IsZeroAt.smul_iff · cited by 1IsZeroAt.smul_iffDFunLike.coe · cited by 62936DFunLike.coeGroup · cited by 6238GroupEquiv.Perm · cited by 1375Equiv.PermtoUnits · cited by 8toUnitsUnits.mulLeft · cited by 6Units.mulLeftEquiv.mulLeftCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by24

Results whose statement or proof uses this declaration.