Theorems · Theorem · field theory
Algebra.IsAlgebraic.trdeg_le_cardinalMk
∀ (R : Type u_1) {A : Type w} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] (s : Set A)
[NoZeroDivisors A] [alg : Algebra.IsAlgebraic (↥(Algebra.adjoin R s)) A], Algebra.trdeg R A ≤ Cardinal.mk ↑s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemstatement and proof · cited by 7,166
- Algebra.algebraMapproof · cited by 4,706
- Cardinalstatement and proof · cited by 2,598
- IsDomainproof · cited by 2,196
- Subalgebrastatement · cited by 1,353
- Cardinal.mkstatement and proof · cited by 942
- NoZeroDivisorsstatement and proof · cited by 545
- Algebra.adjoinstatement and proof · cited by 535
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.isTranscendenceBasis_of_lift_le_trdeg_of_finiteproof · cited by 2