Theorems · Theorem · ring theory
FreeAlgebra.cardinalMk_eq_max_lift
∀ (R : Type u) [inst : CommSemiring R] (X : Type v) [Nonempty X] [Nontrivial R],
Cardinal.mk (FreeAlgebra R X) =
max (max (Cardinal.lift.{v, u} (Cardinal.mk R)) (Cardinal.lift.{u, v} (Cardinal.mk X))) Cardinal.aleph0- Defined in
- Mathlib.Algebra.FreeAlgebra.Cardinality
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Cardinalstatement and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Cardinal.aleph0statement and proof · cited by 521
- FreeMonoidproof · cited by 147
- AlgEquiv.toEquivproof · cited by 65
- FreeAlgebrastatement · cited by 48
- Cardinal.lift_aleph0proof · cited by 41
- sup_assocproof · cited by 37
- Equiv.cardinal_eqproof · cited by 35
Cited by2
Results whose statement or proof uses this declaration.
- FreeAlgebra.cardinalMk_le_max_liftproof · cited by 2
- FreeAlgebra.cardinalMk_eq_maxproof · cited by 0