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]