Theorems · Definition · field theory
IntermediateField.Lifts.union
{F : Type u_1} →
{E : Type u_2} →
{K : Type u_3} →
[inst : Field F] →
[inst_1 : Field E] →
[inst_2 : Field K] →
[inst_3 : Algebra F E] →
[inst_4 : Algebra F K] →
(c : Set (IntermediateField.Lifts F E K)) →
IsChain (fun x1 x2 => x1 ≤ x2) c → IntermediateField.Lifts F E KThe union of a chain of lifts.
- Defined in
- Mathlib.FieldTheory.Extension
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- Bot.botproof · cited by 4,720
- iSupproof · cited by 2,415
- IntermediateFieldproof · cited by 988
- AlgHom.compproof · cited by 501
- AlgEquiv.toAlgHomproof · cited by 273
- Directedproof · cited by 213
- IsChainstatement and proof · cited by 158
- IntermediateField.toSubalgebraproof · cited by 134
Cited by6
Results whose statement or proof uses this declaration.
- IntermediateField.Lifts.le_unionstatement · cited by 3
- IntermediateField.Lifts.nonempty_algHom_of_exist_lifts_finsetproof · cited by 1
- IntermediateField.Lifts.union_isExtendiblestatement and proof · cited by 1
- IntermediateField.Lifts.carrier_unionstatement · cited by 1
- IntermediateField.Lifts.exists_upper_boundproof · cited by 1
- IntermediateField.Lifts.union.congr_simpstatement and proof · cited by 0