sub_prod_sub — Mathlib

English

A bilinear identity for differences of two pairs of maps: (f1 − f2).prod (g1 − g2) = f1.prod g1 − f2.prod g2.

Русский

Алиса равенства: (f1 − f2).prod (g1 − g2) = f1.prod g1 − f2.prod g2.

LaTeX

$$(f1 - f2).prod (g1 - g2) = f1.prod g1 - f2.prod g2$$

Lean4

theorem sub_prod_sub [AddCommGroup M₃] [Module R M₃] [TopologicalSpace M₃] [IsTopologicalAddGroup M₃]
    (f₁ f₂ : ContinuousMultilinearMap R M₁ M₂) (g₁ g₂ : ContinuousMultilinearMap R M₁ M₃) :
    (f₁ - f₂).prod (g₁ - g₂) = f₁.prod g₁ - f₂.prod g₂ :=
  rfl

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