Theorems · Theorem · group theory
AddSubmonoid.LocalizationMap.eq
∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_2} [inst_1 : AddCommMonoid N]
(f : S.LocalizationMap N) {a₁ b₁ : M} {a₂ b₂ : ↥S}, f.mk' a₁ a₂ = f.mk' b₁ b₂ ↔ ∃ c, ↑c + (↑b₂ + a₁) = ↑c + (↑a₂ + b₁)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubmonoid.LocalizationMapstatement and proof · cited by 119
- AddSubmonoid.LocalizationMap.mk'statement · cited by 44
- AddSubmonoid.LocalizationMap.eq_iff_existsproof · cited by 8
- AddSubmonoid.LocalizationMap.mk'_eq_iff_eqproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.eq'proof · cited by 1