ι : Type v
dec_ι : DecidableEq ι
β : ι → Type w
inst✝³ : (i : ι) → AddCommMonoid (β i)
γ : Type u₁
inst✝² : AddCommMonoid γ
M : Type u_1
inst✝¹ : DecidableEq ι
inst✝ : AddCommMonoid M
A : ι → AddSubmonoid M
h : IsInternal A
⊢ Function.Surjective ↑(Dfinsupp.sumAddHom fun i => AddSubmonoid.subtype (A i))
ι : Type v
dec_ι : DecidableEq ι
β : ι → Type w
inst✝³ : (i : ι) → AddCommMonoid (β i)
γ : Type u₁
inst✝² : AddCommMonoid γ
M : Type u_1
inst✝¹ : DecidableEq ι
inst✝ : AddCommMonoid M
A : ι → AddSubmonoid M
h : IsInternal A
⊢ iSup A = ⊤
rw [AddSubmonoid.iSup_eq_mrange_dfinsupp_sumAddHom, AddMonoidHom.mrange_top_iff_surjective]
no goals
ι : Type v
dec_ι : DecidableEq ι
β : ι → Type w
inst✝³ : (i : ι) → AddCommMonoid (β i)
γ : Type u₁
inst✝² : AddCommMonoid γ
M : Type u_1
inst✝¹ : DecidableEq ι
inst✝ : AddCommMonoid M
A : ι → AddSubmonoid M
h : IsInternal A
⊢ Function.Surjective ↑(Dfinsupp.sumAddHom fun i => AddSubmonoid.subtype (A i))
exact Function.Bijective.surjective h