Theorems · Theorem · field theory
Algebra.IsAlgebraic.lift_cardinalMk_le_max
∀ (R : Type u) [inst : CommRing R] [IsDomain R] (L : Type v) [inst_2 : CommRing L] [IsDomain L] [inst_4 : Algebra R L]
[Module.IsTorsionFree R L] [Algebra.IsAlgebraic R L],
Cardinal.lift.{u, v} (Cardinal.mk L) ≤ max (Cardinal.lift.{v, u} (Cardinal.mk R)) Cardinal.aleph0- Defined in
- Mathlib.RingTheory.Algebraic.Cardinality
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Polynomialproof · cited by 5,681
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- IsDomainstatement and proof · cited by 2,196
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Cardinal.mkstatement and proof · cited by 942
- Module.IsTorsionFreestatement and proof · cited by 600
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.cardinalMk_le_maxproof · cited by 3