no goals
G : Type u_1
G' : Type ?u.306276
inst✝⁴ : Group G
inst✝³ : Group G'
A : Type ?u.306285
inst✝² : AddGroup A
H✝ K✝ : Subgroup G
k : Set G
N : Type u_2
inst✝¹ : Group N
P : Type ?u.306312
inst✝ : Group P
H : Subgroup G
K : Subgroup N
J : Subgroup (G × N)
⊢ prod H K ≤ J ↔ map (MonoidHom.inl G N) H ≤ J ∧ map (MonoidHom.inr G N) K ≤ J
simpa only [← Subgroup.toSubmonoid_le] using Submonoid.prod_le_iff