Theorems · Theorem · ring theory
OreLocalization.cardinalMk_le_max
∀ {R : Type u} [inst : Monoid R] (S : Submonoid R) [inst_1 : OreLocalization.OreSet S] (X : Type v)
[inst_2 : MulAction R X],
Cardinal.mk (OreLocalization S X) ≤ max (Cardinal.lift.{v, u} (Cardinal.mk ↥S)) (Cardinal.lift.{u, v} (Cardinal.mk X))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- Finiteproof · cited by 3,029
- Cardinalstatement and proof · cited by 2,598
- mul_commproof · cited by 2,262
- MulActionstatement and proof · cited by 1,294
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Infiniteproof · cited by 352
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement and proof · cited by 90
- OreLocalization.oreDivproof · cited by 72
Cited by1
Results whose statement or proof uses this declaration.
- OreLocalization.cardinalMk_leproof · cited by 2