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Theorems · Theorem · group theory

AddSubmonoid.LocalizationMap.surj

∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_2} [inst_1 : AddCommMonoid N]
  (f : S.LocalizationMap N) (z : N), ∃ x, z + f ↑x.2 = f x.1
Defined in
Mathlib.GroupTheory.MonoidLocalization.Basic
Cited by
7 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Quot.sound
Assumes
AddCommMonoidAddCommMonoid
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Around this declaration

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

AddSubmonoid.LocalizationMap.sec · cited by 20LocalizationMap.secAddSubmonoid.LocalizationMap.sec_spec · cited by 2LocalizationMap.sec_specAddSubmonoid.LocalizationMap.map_isAddRegular · cited by 1LocalizationMap.map_isAdd…AddSubmonoid.LocalizationMap.surj₂ · cited by 1LocalizationMap.surj₂AddSubmonoid.LocalizationMap.isCancelAdd · cited by 0LocalizationMap.isCancelA…AddSubmonoid.LocalizationMap.lift_injective_iff · cited by 0LocalizationMap.lift_inje…AddSubmonoid.LocalizationMap.epic_of_localizationMap · cited by 0LocalizationMap.epic_of_l…AddSubmonoid.LocalizationMap.lift_surjective_iff · cited by 0LocalizationMap.lift_surj…DFunLike.coe · cited by 62936DFunLike.coeAddCommMonoid · cited by 12281AddCommMonoidAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.LocalizationMap · cited by 119AddSubmonoid.Localization…AddSubmonoid.LocalizationMap.isLocalizationMap · cited by 5LocalizationMap.isLocaliz…AddSubmonoid.IsLocalizationMap.surj · cited by 5IsLocalizationMap.surjLocalizationMap.surjCITED BYCITES

Cites6

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Cited by8

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