Theorems · Theorem · field theory
Field.Emb.Cardinal.directed_filtration
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E]
[rank_inf : Fact (Cardinal.aleph0 ≤ Module.rank F E)] [inst_3 : Algebra.IsAlgebraic F E]
{i : WithTop (Module.rank F E).ord.ToType}, Directed (fun x1 x2 => x1 ≤ x2) fun j => Field.Emb.Cardinal.filtration ↑j- Defined in
- Mathlib.FieldTheory.CardinalEmb
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement · cited by 7,166
- WithTopstatement and proof · cited by 3,754
- Factstatement and proof · cited by 2,726
- Cardinalstatement · cited by 2,598
- Set.Iiostatement and proof · cited by 1,166
- IntermediateFieldstatement · cited by 988
- OrderEmbeddingstatement · cited by 619
- Cardinal.aleph0statement and proof · cited by 521
Cited by1
Results whose statement or proof uses this declaration.
- Field.Emb.Cardinal.equivLimproof · cited by 1