Theorems · Theorem · field theory

IntermediateField.Lifts.union_isExtendible

∀ {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))
  (hc : IsChain (fun x1 x2 => x1 ≤ x2) c) [alg : Algebra.IsAlgebraic F E] [Nonempty ↑c],
  (∀ σ ∈ c, σ.IsExtendible) → (IntermediateField.Lifts.union c hc).IsExtendible

Defined in: Mathlib.FieldTheory.Extension
Cited by: 1 results in Mathlib
Foundations: Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Field Algebra Algebra Algebra.IsAlgebraic Nonempty

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IntermediateField.Lifts.nonempty_algHom_of_exist_lifts_finsetproof · cited by 1