Theorems · Theorem · ring theory
AddOreLocalization.oreSub_eq_iff
∀ {R : Type u_1} [inst : AddMonoid R] {S : AddSubmonoid R} [inst_1 : AddOreLocalization.AddOreSet S] {X : Type u_2}
[inst_2 : AddAction R X] {r₁ r₂ : X} {s₁ s₂ : ↥S}, r₁ -ₒ s₁ = r₂ -ₒ s₂ ↔ ∃ u v, u +ᵥ r₂ = v +ᵥ r₁ ∧ ↑u + ↑s₂ = v + ↑s₁- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- HVAdd.hVAddstatement · cited by 1,820
- AddSubmonoidstatement and proof · cited by 1,178
- AddActionstatement and proof · cited by 820
- AddOreLocalization.AddOreSetstatement and proof · cited by 50
- AddOreLocalizationstatement · cited by 44
- Quotient.eq''proof · cited by 44
- AddOreLocalization.oreSubstatement · cited by 40
Cited by5
Results whose statement or proof uses this declaration.
- AddLocalization.mk_eq_mk_iffproof · cited by 5
- AddOreLocalization.oreSub_zero_surjective_of_finite_leftproof · cited by 2
- AddOreLocalization.oreSub_zero_surjective_of_finite_rightproof · cited by 2
- AddOreLocalization.sub_eq_zero'proof · cited by 1
- AddOreLocalization.cardinalMk_le_lift_cardinalMk_of_addCommuteproof · cited by 0