Theorems · Theorem · field theory
Field.Emb.cardinal_eq_of_isSeparable
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.IsSeparable F E],
Cardinal.mk (Field.Emb F E) = (fun c => if Cardinal.aleph0 ≤ c then 2 ^ c else c) (Module.rank F E)- Defined in
- Mathlib.FieldTheory.CardinalEmb
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Cardinalstatement and proof · cited by 2,598
- Module.finrankproof · cited by 1,770
- LT.lt.ne'proof · cited by 1,417
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.aleph0statement and proof · cited by 521
- Module.rankstatement and proof · cited by 496
- Algebra.IsSeparablestatement and proof · cited by 210
- Module.finrank_posproof · cited by 62
- Module.finrank_eq_rankproof · cited by 29
- Field.Embstatement and proof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Field.Emb.cardinal_eqproof · cited by 0