Theorems · Theorem · group theory
AddLocalization.addEquivOfQuotient_symm_addMonoidOf
∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_2} [inst_1 : AddCommMonoid N]
{f : S.LocalizationMap N} (x : M),
(AddLocalization.addEquivOfQuotient f).symm (f x) = (AddLocalization.addMonoidOf S) x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidAddCommMonoid
Around this declaration
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Cites11
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
- AddEquivstatement · cited by 1,087
- AddEquiv.symmstatement · cited by 530
- AddSubmonoid.LocalizationMapstatement and proof · cited by 119
- AddLocalizationstatement · cited by 38
- AddSubmonoid.LocalizationMap.map_addUnitsproof · cited by 36
- AddLocalization.addMonoidOfstatement and proof · cited by 13
- AddSubmonoid.LocalizationMap.lift_eqproof · cited by 8
- AddLocalization.addEquivOfQuotientstatement · cited by 7
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