ofComponents_fst — Mathlib

English

The composition of Biprod.ofComponents with another Biprod.ofComponents equals a Biprod.ofComponents of the bilinear matrix product.

Русский

Сочетание Biprod.ofComponents с другой Biprod.ofComponents даёт Biprod.ofComponents от произведения по элементам матрицы.

LaTeX

$$Biprod.ofComponents f11 f12 f21 f22 ≫ Biprod.ofComponents g11 g12 g21 g22 = Biprod.ofComponents (f11 ≫ g11 + f12 ≫ g21) (f11 ≫ g12 + f12 ≫ g22) (f21 ≫ g11 + f22 ≫ g21) (f21 ≫ g12 + f22 ≫ g22)$$

Lean4

@[simp]
theorem ofComponents_fst : Biprod.ofComponents f₁₁ f₁₂ f₂₁ f₂₂ ≫ biprod.fst = biprod.fst ≫ f₁₁ + biprod.snd ≫ f₂₁ := by
  simp [Biprod.ofComponents]

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