Theorems · Theorem · group theory
AddLocalization.r_iff_exists
∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {x y : M × ↥S},
(AddLocalization.r S) x y ↔ ∃ c, ↑c + (↑y.2 + x.1) = ↑c + (↑x.2 + y.1)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoid
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 and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- AddConstatement · cited by 138
- AddLocalization.rstatement · cited by 14
- AddCon.rel_mkproof · cited by 4
- AddLocalization.r_eq_r'proof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.eq'proof · cited by 1
- AddLocalization.mk_eq_mk_iff'proof · cited by 1
- AddLocalization.r_iff_oreEqv_rproof · cited by 1
- AddLocalization.mk_left_injectiveproof · cited by 1
- AddLocalization.r_of_eqproof · cited by 0