linearDisjoint_comm' — Mathlib

English

A higher-order preservation lemma: linear disjointness is preserved by algebra homomorphisms in even more elaborate tower arrangements.

Русский

Еще одно лемматическое утверждение сохранения: линейная независимость сохраняется гомоморфизмами алгебры в сложной башне.

LaTeX

$$$\\text{(map'')} : \\text{preservation under maps with multiple towers}$$$

Lean4

/-- Linear disjointness is symmetric. -/
theorem linearDisjoint_comm' :
    (IsScalarTower.toAlgHom F L E).fieldRange.LinearDisjoint L' ↔
      (IsScalarTower.toAlgHom F L' E).fieldRange.LinearDisjoint L :=
  ⟨LinearDisjoint.symm', LinearDisjoint.symm'⟩

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