Theorems · Theorem · ring theory
OreLocalization.cardinalMk
∀ {R : Type u} [inst : Ring R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S],
S ≤ nonZeroDivisorsLeft R → Cardinal.mk (OreLocalization S R) = Cardinal.mk R- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingOreLocalization.OreSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Submonoidstatement and proof · cited by 3,086
- Cardinalstatement · cited by 2,598
- le_antisymmproof · cited by 2,068
- Cardinal.mkstatement · cited by 942
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement · cited by 90
- nonZeroDivisorsLeftstatement and proof · cited by 26
- Cardinal.mk_le_of_injectiveproof · cited by 12
- OreLocalization.cardinalMk_leproof · cited by 2
- OreLocalization.numeratorHom_injproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Localization.cardinalMkproof · cited by 1