Theorems · Theorem · field theory
AlgebraicIndependent.lift_cardinalMk_le_trdeg
∀ {ι : Type u} {R : Type u_2} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Nontrivial R],
AlgebraicIndependent R x → Cardinal.lift.{v, u} (Cardinal.mk ι) ≤ Cardinal.lift.{u, v} (Algebra.trdeg R A)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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.rangeproof · cited by 4,705
- Cardinalstatement and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- le_rflproof · cited by 1,558
- Cardinal.mkstatement · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- AlgebraicIndependentstatement and proof · cited by 120
- Cardinal.lift_leproof · cited by 78
- Equiv.ofInjectiveproof · cited by 64
- Algebra.trdegstatement and proof · cited by 39
Cited by4
Results whose statement or proof uses this declaration.
- lift_trdeg_le_of_surjectiveproof · cited by 3
- lift_trdeg_le_of_injectiveproof · cited by 2
- AlgebraicIndependent.cardinalMk_le_trdegproof · cited by 0
- finite_of_algebraicIndependentproof · cited by 0