Theorem: DividedPowerAlgebra.dp_mul (unused_files/Init_copy.lean)

State before:
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n p : ℕ
m : M
⊢ dp R n m * dp R p m = (n + p).choose n • dp R (n + p) m
Tactic:
simp only [dp_def, ← _root_.map_mul, ← map_nsmul]
State after:
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n p : ℕ
m : M
⊢ (mkAlgHom R (Rel R M)) (X (n, m)) * (mkAlgHom R (Rel R M)) (X (p, m)) =
    (n + p).choose n • (mkAlgHom R (Rel R M)) (X (n + p, m))