no goals
G : Type u_1
G' : Type ?u.303912
inst✝⁴ : Group G
inst✝³ : Group G'
A : Type ?u.303921
inst✝² : AddGroup A
H✝ K✝ : Subgroup G
k : Set G
N : Type u_2
inst✝¹ : Group N
P : Type ?u.303948
inst✝ : Group P
H : Subgroup G
K : Subgroup N
J : Subgroup (G × N)
⊢ J ≤ prod H K ↔ map (MonoidHom.fst G N) J ≤ H ∧ map (MonoidHom.snd G N) J ≤ K
simpa only [← Subgroup.toSubmonoid_le] using Submonoid.le_prod_iff