C_smul_derivation_apply — Mathlib

English

The derivation mkDerivation sends the polynomial X to the scalar a when applied to X.

Русский

Производная mkDerivation отправляет многочлен X в скаляр a при приложении к X.

LaTeX

$$$mkDerivation\ R\ a\ X = a$$$

Lean4

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

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