pair_neg_right_iff — Mathlib

English

If v and v' are linearly independent, then the combined map via Sum.elim (inl ∘ v) (inr ∘ v') is linearly independent.

Русский

Если v и v' линейно независимы, то объединение через Sum.elim остаётся линейно независимым.

LaTeX

$$$\\mathrm{LinearIndependent}_R(\\mathrm{Sum.elim}(\\mathrm{inl}\\circ v)(\\mathrm{inr}\\circ v'))$$$

Lean4

@[simp]
theorem pair_neg_right_iff : LinearIndependent R ![x, -y] ↔ LinearIndependent R ![x, y] := by
  rw [pair_symm_iff, pair_neg_left_iff, pair_symm_iff]

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