no goals
M : Type u_1
N : Type ?u.1028
inst✝¹ : Monoid M
inst✝ : AddMonoid N
P : Submonoid M
x✝ : ∃ S, closure S = P ∧ Set.Finite S
S : Set M
hS : closure S = P
hf : Set.Finite S
⊢ closure ↑(Set.Finite.toFinset hf) = P
simp [hS]