no goals
G : Type u_1
G' : Type ?u.308406
inst✝⁴ : Group G
inst✝³ : Group G'
A : Type ?u.308415
inst✝² : AddGroup A
H✝ K✝ : Subgroup G
k : Set G
N : Type u_2
inst✝¹ : Group N
P : Type ?u.308442
inst✝ : Group P
H : Subgroup G
K : Subgroup N
⊢ prod H K = ⊥ ↔ H = ⊥ ∧ K = ⊥
simpa only [← Subgroup.toSubmonoid_eq] using Submonoid.prod_eq_bot_iff