symm — Mathlib

English

Linear disjointness is symmetric: A and B are linearly disjoint iff B and A are.

Русский

Линейная независимость симметрична: A и B линейно неразделимы тогда и только тогда, когда B и A.

LaTeX

$$$A.LinearDisjoint B \\iff B.LinearDisjoint A.$$$

Lean4

/-- Linear disjointness is symmetric. -/
theorem symm (H : A.LinearDisjoint B) : B.LinearDisjoint A :=
  linearDisjoint_iff'.2 (linearDisjoint_iff'.1 H).symm

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