Theorems · Theorem · group theory
Submonoid.LocalizationMap.map_right_cancel
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoid N]
(f : S.LocalizationMap N) {x y : M} {c : ↥S}, f (↑c * x) = f (↑c * y) → f x = f y- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Submonoidstatement and proof · cited by 3,086
- Unitsproof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Units.valproof · cited by 1,966
- IsUnitproof · cited by 1,602
- map_mulproof · cited by 1,137
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Submonoid.LocalizationMap.map_unitsproof · cited by 46
- Units.mul_right_injproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.map_left_cancelproof · cited by 1
- IsLocalization.map_right_cancelproof · cited by 0