rescale_rescale — Mathlib

English

The composition of substitutions equals the substitution with the composed rule: (subst b) ∘ (subst a) = subst (R := R) (fun s ↦ subst b (a s)).

Русский

Композиция подстановок равна подстановке по композиции правил: (subst b) ∘ (subst a) = subst (R := R) (λ s. subst b (a s)).

LaTeX

$$$\operatorname{subst}\, b \circ \operatorname{subst}\, a = \operatorname{subst}\, (R := R) (\lambda s. \operatorname{subst}\, b (a\,s))$$$

Lean4

theorem rescale_rescale (f : MvPowerSeries σ R) (a b : σ → R) : rescale b (rescale a f) = rescale (a * b) f :=
  by
  ext n
  simp [← mul_assoc, mul_pow, mul_comm]

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