Theorems · Theorem · field theory
Field.Emb.cardinal_eq_two_pow_rank
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.IsSeparable F E],
Cardinal.aleph0 ≤ Module.rank F E → Cardinal.mk (Field.Emb F E) = 2 ^ Module.rank F E- Defined in
- Mathlib.FieldTheory.CardinalEmb
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Factproof · cited by 2,726
- Cardinalstatement and proof · cited by 2,598
- LT.lt.leproof · cited by 2,189
- le_antisymmproof · cited by 2,068
- WithTop.someproof · cited by 1,128
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.aleph0statement and proof · cited by 521
- Module.rankstatement and proof · cited by 496
- Cardinal.ordproof · cited by 266
- Algebra.IsSeparablestatement and proof · cited by 210
Cited by2
Results whose statement or proof uses this declaration.
- Field.Emb.cardinal_eq_of_isSeparableproof · cited by 1
- Field.Emb.cardinal_eq_two_pow_sepDegreeproof · cited by 0