Theorems · Definition · field theory
Field.Emb.Cardinal.wellOrderedBasis
(F : Type u) →
(E : Type v) →
[inst : Field F] → [inst_1 : Field E] → [inst_2 : Algebra F E] → Module.Basis (Module.rank F E).ord.ToType F EA basis of E/F indexed by the initial ordinal.
- Defined in
- Mathlib.FieldTheory.CardinalEmb
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Equiv.symmproof · cited by 3,681
- Module.Basisstatement · cited by 1,477
- Module.rankstatement · cited by 496
- Nonempty.someproof · cited by 340
- Cardinal.ordstatement · cited by 266
- Ordinal.ToTypestatement · cited by 143
- Module.Free.chooseBasisproof · cited by 121
- Module.Basis.reindexproof · cited by 57
Cited by17
Results whose statement or proof uses this declaration.
- Field.Emb.Cardinal.leastExtproof · cited by 13
- Field.Emb.Cardinal.filtrationproof · cited by 7
- Field.Emb.Cardinal.isLeast_leastExtstatement and proof · cited by 4
- Field.Emb.Cardinal.deg_lt_aleph0statement and proof · cited by 2
- Field.Emb.Cardinal.factorproof · cited by 2
- Field.Emb.Cardinal.strictMono_leastExtproof · cited by 2
- Field.Emb.Cardinal.adjoin_image_leastExtstatement and proof · cited by 1
- Field.Emb.Cardinal.iSup_adjoin_eq_topstatement and proof · cited by 1
- Field.Emb.Cardinal.strictMono_filtrationstatement and proof · cited by 1
- Field.Emb.Cardinal.succEquivstatement and proof · cited by 1
- Field.Emb.Cardinal.succEquiv_coherencestatement and proof · cited by 1
- Field.Emb.Cardinal.two_le_degstatement and proof · cited by 1