rescaleUnit — Mathlib

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

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