English
For ha and hb substitutions and a polynomial f, the composed substitution applied to f equals applying the two substitutions in sequence.
Русский
Для подстановок ha и hb и полинома f применяем композицию подстановок к f точно как последовательное применение двух подстановок.
LaTeX
$$$\\text{PowerSeries.subst}(b, \\text{PowerSeries.subst}(a, f)) = \\text{PowerSeries.subst}(\\text{PowerSeries.subst}(b, a), f)$$$
Lean4
theorem _root_.MvPowerSeries.rescaleUnit (a : R) (f : R⟦X⟧) :
MvPowerSeries.rescale (Function.const _ a) f = rescale a f :=
by
ext d
rw [coeff_rescale, coeff, MvPowerSeries.coeff_rescale]
simp