Mathlib Map

Theorems · Definition · group theory

Equiv.addLeft

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

Left addition in an AddGroup 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
AddGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Homeomorph.addLeft · cited by 20Homeomorph.addLeftOrderIso.addLeft · cited by 18OrderIso.addLeftIsometryEquiv.addLeft · cited by 3IsometryEquiv.addLeftAddChar.sum_eq_ite · cited by 3AddChar.sum_eq_iteisImmersionOfComplement_subtypeVal_Icc · cited by 3isImmersionOfComplement_s…Equiv.addLeft_symm · cited by 2Equiv.addLeft_symmHomeomorph.shearAddRight · cited by 2Homeomorph.shearAddRightAddGroup.addLeft_bijective · cited by 2AddGroup.addLeft_bijectiveMeasurableEquiv.shearAddRight · cited by 1MeasurableEquiv.shearAddR…comap_addConj_nhds_zero · cited by 1comap_addConj_nhds_zeroEquiv.nsmul_addLeft · cited by 1Equiv.nsmul_addLeftAddSubgroup.normalCore_eq_iInf_map_addConj · cited by 1AddSubgroup.normalCore_eq…roth_3ap_theorem · cited by 1roth_3ap_theoremEquiv.neg_addLeft · cited by 1Equiv.neg_addLeftEquiv.zsmul_addLeft · cited by 1Equiv.zsmul_addLeftDFunLike.coe · cited by 62936DFunLike.coeAddGroup · cited by 4410AddGroupEquiv.Perm · cited by 1375Equiv.PermtoAddUnits · cited by 8toAddUnitsAddUnits.addLeft · cited by 3AddUnits.addLeftEquiv.addLeftCITED 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.