case zero
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
⊢ derivedSeries G Nat.zero ≤ lowerCentralSeries G Nat.zero

case succ
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
i : ℕ
ih : derivedSeries G i ≤ lowerCentralSeries G i
⊢ derivedSeries G (Nat.succ i) ≤ lowerCentralSeries G (Nat.succ i)
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
n : ℕ
⊢ derivedSeries G n ≤ lowerCentralSeries G n
induction' n with i ih
no goals
case zero
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
⊢ derivedSeries G Nat.zero ≤ lowerCentralSeries G Nat.zero
simp
case succ
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
i : ℕ
ih : derivedSeries G i ≤ lowerCentralSeries G i
⊢ derivedSeries G i ≤ ⊤
case succ
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
i : ℕ
ih : derivedSeries G i ≤ lowerCentralSeries G i
⊢ derivedSeries G (Nat.succ i) ≤ lowerCentralSeries G (Nat.succ i)
apply commutator_mono ih
no goals
case succ
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
i : ℕ
ih : derivedSeries G i ≤ lowerCentralSeries G i
⊢ derivedSeries G i ≤ ⊤
simp