snd — Mathlib

English

The isometry that embeds Q1 into Q1.prod Q2 and the corresponding embedding of Q2 into the product are compatible with sums and projections.

Русский

Изометрии включения в левую часть и правую часть совместимы с операциями суммы и проекции.

LaTeX

$$equivalent to standard orthogonality lemmas: fst and inl interactions; snd and inr interactions.$$

Lean4

/-- `LinearMap.snd` as an isometry, when the first space has the zero quadratic form. -/
@[simps!]
def snd (Q₂ : QuadraticMap R M₂ P) : ((0 : QuadraticMap R M₁ P).prod Q₂) →qᵢ Q₂
    where
  toLinearMap := LinearMap.snd R _ _
  map_app' m₁ := by simp

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