Theorems · Theorem · field theory
finTrdeg_iff_trdeg
∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L],
FinTrdeg K L ↔ Algebra.trdeg K L < Cardinal.aleph0- Defined in
- Mathlib.FieldTheory.FinTrdeg
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.rangeproof · cited by 4,705
- Submonoidproof · cited by 3,086
- add_zeroproof · cited by 2,707
- Cardinalstatement and proof · cited by 2,598
- Set.Finiteproof · cited by 1,814
- Subalgebraproof · cited by 1,353
- IntermediateFieldproof · cited by 988
- IsLocalizationproof · cited by 636
- Cardinal.aleph0statement and proof · cited by 521
Cited by4
Results whose statement or proof uses this declaration.
- trdeg_lt_aleph0proof · cited by 3
- FinTrdeg.of_trdegproof · cited by 0
- FinTrdeg.transproof · cited by 0
- FinTrdeg.of_isTranscendenceBasisproof · cited by 0