F : Type ?u.346509
α : Type u_1
β : Type ?u.346515
γ : Type ?u.346518
ι : Type ?u.346521
κ : Type ?u.346524
inst✝ : LinearOrder α
s✝ : Finset α
H : Finset.Nonempty s✝
x : α
s : Finset αᵒᵈ
⊢ WithTop.map (↑ofDual) (Finset.min s) = sup s (WithBot.some ∘ ↑ofDual)
F : Type ?u.346509
α : Type u_1
β : Type ?u.346515
γ : Type ?u.346518
ι : Type ?u.346521
κ : Type ?u.346524
inst✝ : LinearOrder α
s✝ : Finset α
H : Finset.Nonempty s✝
x : α
s : Finset αᵒᵈ
⊢ WithTop.map (↑ofDual) (Finset.min s) = Finset.max (image (↑ofDual) s)
rw [max_eq_sup_withBot, sup_image]
no goals
F : Type ?u.346509
α : Type u_1
β : Type ?u.346515
γ : Type ?u.346518
ι : Type ?u.346521
κ : Type ?u.346524
inst✝ : LinearOrder α
s✝ : Finset α
H : Finset.Nonempty s✝
x : α
s : Finset αᵒᵈ
⊢ WithTop.map (↑ofDual) (Finset.min s) = sup s (WithBot.some ∘ ↑ofDual)
exact congr_fun Option.map_id _