case h
R : Type u_1
inst✝ : CommSemiring R
f : PowerSeries R
a b : R
n : ℕ
⊢ ↑(coeff R n) (↑(rescale b) (↑(rescale a) f)) = ↑(coeff R n) (↑(rescale (a * b)) f)
R : Type u_1
inst✝ : CommSemiring R
f : PowerSeries R
a b : R
⊢ ↑(rescale b) (↑(rescale a) f) = ↑(rescale (a * b)) f
ext n
case h
R : Type u_1
inst✝ : CommSemiring R
f : PowerSeries R
a b : R
n : ℕ
⊢ b ^ n * (a ^ n * ↑(coeff R n) f) = (a * b) ^ n * ↑(coeff R n) f
case h
R : Type u_1
inst✝ : CommSemiring R
f : PowerSeries R
a b : R
n : ℕ
⊢ ↑(coeff R n) (↑(rescale b) (↑(rescale a) f)) = ↑(coeff R n) (↑(rescale (a * b)) f)
simp_rw [coeff_rescale]
no goals
case h
R : Type u_1
inst✝ : CommSemiring R
f : PowerSeries R
a b : R
n : ℕ
⊢ b ^ n * (a ^ n * ↑(coeff R n) f) = (a * b) ^ n * ↑(coeff R n) f
rw [mul_pow, mul_comm _ (b ^ n), mul_assoc]