instModule — Mathlib

English

The additive structure is coherent with scalar action and addition on arguments.

Русский

Аддитивная структура согласована с действием скаляра и сложением аргументов.

LaTeX

$$Proofs showing associativity, commutativity and zero/identity laws for addition on polynomial laws.$$

Lean4

instance : Module R (M →ₚₗ[R] N) where
  smul_zero a := rfl
  smul_add a f g := by ext; simp only [smul_def, add_def, smul_add]
  add_smul := add_smul
  zero_smul := zero_smul

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