case intro
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
h : Group.IsNilpotent (G ⧸ center G)
n : ℕ
hn : upperCentralSeries (G ⧸ center G) n = ⊤
⊢ Group.IsNilpotent G
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
h : Group.IsNilpotent (G ⧸ center G)
⊢ Group.IsNilpotent G
obtain ⟨n, hn⟩ := h.nilpotent
case intro
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
h : Group.IsNilpotent (G ⧸ center G)
n : ℕ
hn : upperCentralSeries (G ⧸ center G) n = ⊤
⊢ upperCentralSeries G (Nat.succ n) = ⊤
case intro
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
h : Group.IsNilpotent (G ⧸ center G)
n : ℕ
hn : upperCentralSeries (G ⧸ center G) n = ⊤
⊢ Group.IsNilpotent G
use n.succ
no goals
case intro
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : Normal H
h : Group.IsNilpotent (G ⧸ center G)
n : ℕ
hn : upperCentralSeries (G ⧸ center G) n = ⊤
⊢ upperCentralSeries G (Nat.succ n) = ⊤
simp [← comap_upperCentralSeries_quotient_center, hn]