Theorems · Theorem · group theory
AddSubmonoid.LocalizationMap.map_addUnits
∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_2} [inst_1 : AddCommMonoid N]
(f : S.LocalizationMap N) (y : ↥S), IsAddUnit (f ↑y)- Cited by
- 36 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoidAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- IsAddUnitstatement · cited by 215
- AddSubmonoid.LocalizationMapstatement and proof · cited by 119
- AddSubmonoid.LocalizationMap.isLocalizationMapproof · cited by 5
- AddSubmonoid.IsLocalizationMap.map_addUnitsproof · cited by 4
Cited by38
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.mk'proof · cited by 44
- AddSubmonoid.LocalizationMap.eq_iff_existsproof · cited by 8
- AddSubmonoid.LocalizationMap.addEquivOfLocalizationsproof · cited by 8
- AddSubmonoid.LocalizationMap.mk'_eq_iff_eqproof · cited by 4
- AddLocalization.mk_eq_addMonoidOf_mk'_applyproof · cited by 3
- AddSubmonoid.LocalizationMap.mk'_secproof · cited by 3
- AddSubmonoid.LocalizationMap.mk'_specproof · cited by 3
- AddSubmonoid.LocalizationMap.eq_mk'_iff_add_eqproof · cited by 2
- AddSubmonoid.LocalizationMap.lift_idstatement · cited by 2
- AddSubmonoid.LocalizationMap.map_add_rightproof · cited by 2
- AddSubmonoid.LocalizationMap.map_eqproof · cited by 2
- AddSubmonoid.LocalizationMap.mk'_self'proof · cited by 2