Theorems · Theorem · field theory
Field.Emb.cardinal_separableClosure
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.IsAlgebraic F E], Cardinal.mk (Field.Emb F ↥(separableClosure F E)) = Cardinal.mk (Field.Emb F E)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- mul_oneproof · cited by 3,885
- Cardinalstatement and proof · cited by 2,598
- IntermediateFieldstatement · cited by 988
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftproof · cited by 583
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Cardinal.lift_idproof · cited by 163
- separableClosurestatement and proof · cited by 55
- Equiv.cardinal_eqproof · cited by 35
- Cardinal.lift_oneproof · cited by 33
Cited by2
Results whose statement or proof uses this declaration.
- Field.Emb.cardinal_eqproof · cited by 0
- Field.Emb.cardinal_eq_two_pow_sepDegreeproof · cited by 0