associated_neg_proof — Mathlib

English

If 2 is invertible, the quadratic map associated to the negation of Q is the associated quadratic map of −Q, giving (−Q).toQuadraticMap = Q − Q′ with h connecting B to Q′ − Q.

Русский

При обратимости 2 получаем: ассоциированная квадратичная карта для −Q равна −Q′; тождество: (−Q).toQuadraticMap = 0 − Q.

LaTeX

$$$ (\text{QuadraticMap.associated}(-Q)).toQuadraticMap = 0 - Q $$$

Lean4

theorem associated_neg_proof [Invertible (2 : R)] :
    (QuadraticMap.associated (R := R) (M := M) (-Q)).toQuadraticMap = 0 - Q := by
  simp [QuadraticMap.toQuadraticMap_associated]

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