no goals
ι : Type ?u.13107
α : Type u_1
M : Type ?u.13113
N : Type ?u.13116
P : Type ?u.13119
M₀ : Type ?u.13122
G : Type ?u.13125
R : Type ?u.13128
inst✝ : CommGroup α
l₂ : List α
⊢ alternatingProd ([] ++ l₂) = alternatingProd [] * alternatingProd l₂ ^ (-1) ^ length []
simp
no goals
ι : Type ?u.13107
α : Type u_1
M : Type ?u.13113
N : Type ?u.13116
P : Type ?u.13119
M₀ : Type ?u.13122
G : Type ?u.13125
R : Type ?u.13128
inst✝ : CommGroup α
a : α
l₁ l₂ : List α
⊢ alternatingProd (a :: l₁ ++ l₂) = alternatingProd (a :: l₁) * alternatingProd l₂ ^ (-1) ^ length (a :: l₁)
simp_rw [cons_append, alternatingProd_cons, alternatingProd_append, length_cons, pow_succ,
  neg_mul, one_mul, zpow_neg, ← div_eq_mul_inv, div_div]