rw [Finset.card_image_of_injOn]
G : Type u_1
inst✝ : Group G
g : G
h : IsOfFinOrder g
this : orderOf g ≠ 0
⊢ (Finset.image (fun i => g ^ i) (Set.toFinset (Set.Ico 0 (orderOf g)))).card = orderOf g
G : Type u_1
inst✝ : Group G
g : G
h : IsOfFinOrder g
this : orderOf g ≠ 0
⊢ (Set.toFinset (Set.Ico 0 (orderOf g))).card = orderOf g

G : Type u_1
inst✝ : Group G
g : G
h : IsOfFinOrder g
this : orderOf g ≠ 0
⊢ Set.InjOn (fun i => g ^ i) ↑(Set.toFinset (Set.Ico 0 (orderOf g)))