linearDisjoint_comm — Mathlib

English

Linear disjointness is preserved by algebra homomorphisms: if A is disjoint from L, so is A.map f from A to a codomain under f.

Русский

Линейная независимость сохраняется под абелевыми гомоморфизмами: если A неразделимо от L, то и образ A под f неразделим от L.

LaTeX

$$$H : A.LinearDisjoint L \\Rightarrow (A.map f) .LinearDisjoint L.$$$

Lean4

/-- Linear disjointness is symmetric. -/
theorem linearDisjoint_comm : A.LinearDisjoint B ↔ B.LinearDisjoint A :=
  ⟨LinearDisjoint.symm, LinearDisjoint.symm⟩

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