derivation_C_mul — Mathlib

English

Multiplication by a constant commutes with the derivation action of mkDerivation on f.

Русский

Умножение на константу commuting с действием производной mkDerivation на f.

LaTeX

$$$\\\\mathrm{C}(a) \\cdot Df = a \\cdot Df$$$

Lean4

@[simp]
theorem derivation_C_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
    C (σ := σ) a • D f = a • D f :=
  by
  have : C (σ := σ) a • D f = D (C a * f) := by simp
  rw [this, C_mul', D.map_smul]

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