of_le' — Mathlib

English

A variant allowing abstract fields; Lefter shows disjointness preserved under left embedding.

Русский

Вариант с абстрактными полями; сохранение разобщенности под левым вложением.

LaTeX

$$$A \perp L'\Rightarrow A \perp L$ (under structure)$$

Lean4

/-- Similar to `IntermediateField.LinearDisjoint.of_le` but this is for abstract fields. -/
theorem of_le' {A' : IntermediateField F E} (H : A.LinearDisjoint L) (hA : A' ≤ A) (L' : Type*) [Field L']
    [Algebra F L'] [Algebra L' L] [IsScalarTower F L' L] [Algebra L' E] [IsScalarTower F L' E] [IsScalarTower L' L E] :
    A'.LinearDisjoint L' :=
  H.of_le_left hA |>.of_le_right' L'

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