Theorems · Theorem · ring theory
AddOreLocalization.oreSub_nsmul
∀ {R : Type u_1} [inst : AddMonoid R] {S : AddSubmonoid R} [inst_1 : AddOreLocalization.AddOreSet S] (r : R) (s : ↥S)
(n : ℕ), AddCommute r ↑s → n • (r -ₒ s) = n • r -ₒ n • s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- AddSubmonoidstatement and proof · cited by 1,178
- AddCommutestatement and proof · cited by 185
- zero_nsmulproof · cited by 137
- succ_nsmulproof · cited by 65
- AddOreLocalization.AddOreSetstatement and proof · cited by 50
- AddOreLocalizationstatement and proof · cited by 44
- AddOreLocalization.oreSubstatement and proof · cited by 40
- succ_nsmul'proof · cited by 25
- AddCommute.symmproof · cited by 18
- AddOreLocalization.oreSub_add_charproof · cited by 8
- AddOreLocalization.zero_defproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AddLocalization.mk_nsmulproof · cited by 0