Theorems · Theorem · commutative algebra
IsLocalization.lift_id
∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} {S : Type u_2} [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [inst_3 : IsLocalization M S] (x : S), (IsLocalization.lift ⋯) x = x- Defined in
- Mathlib.RingTheory.Localization.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- IsLocalization.map_unitsstatement · cited by 69
- IsLocalization.toLocalizationMapproof · cited by 69
- IsLocalization.liftstatement · cited by 27
- Submonoid.LocalizationMap.lift_idproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.map_idproof · cited by 1
- galLift_idproof · cited by 0