linearDisjoint_comm — Mathlib

English

In a commutative setting, the linear disjointness relation between A and B is symmetric: A.LinearDisjoint B ↔ B.LinearDisjoint A.

Русский

В коммутативной установке отношение линейной дизъюнктности между A и B симметрично: A.LinearDisjoint B ↔ B.LinearDisjoint A.

LaTeX

$$$A.LinearDisjoint B \leftrightarrow B.LinearDisjoint A$$$

Lean4

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

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