Mathlib Map

Theorems · Theorem · group theory

AddSubmonoid.LocalizationMap.lift_id

∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_2} [inst_1 : AddCommMonoid N]
  (f : S.LocalizationMap N) (x : N), (f.lift ⋯) x = x
Defined in
Mathlib.GroupTheory.MonoidLocalization.Maps
Cited by
2 results in Mathlib
Foundations
Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidAddCommMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddSubmonoid.LocalizationMap.map_id · cited by 0LocalizationMap.map_idAddSubmonoid.LocalizationMap.lift_left_inverse · cited by 0LocalizationMap.lift_left…DFunLike.coe · cited by 62936DFunLike.coeAddCommMonoid · cited by 12281AddCommMonoidAddMonoidHom · cited by 3230AddMonoidHomAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.LocalizationMap · cited by 119AddSubmonoid.Localization…AddMonoidHom.id · cited by 107AddMonoidHom.idDFunLike.ext_iff · cited by 102DFunLike.ext_iffAddSubmonoid.LocalizationMap.map_addUnits · cited by 36LocalizationMap.map_addUn…AddSubmonoid.LocalizationMap.toAddMonoidHom · cited by 29LocalizationMap.toAddMono…AddSubmonoid.LocalizationMap.lift · cited by 23LocalizationMap.liftAddSubmonoid.LocalizationMap.lift_of_comp · cited by 2LocalizationMap.lift_of_c…LocalizationMap.lift_idCITED BYCITES

Cites11

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

Cited by2

Results whose statement or proof uses this declaration.