F : Type ?u.347556
α : Type u_1
β : Type ?u.347562
γ : Type ?u.347565
ι : Type ?u.347568
κ : Type ?u.347571
inst✝ : LinearOrder α
s✝ : Finset α
H : Finset.Nonempty s✝
x : α
s : Finset αᵒᵈ
⊢ WithBot.map (↑ofDual) (Finset.max s) = inf s (WithTop.some ∘ ↑ofDual)
F : Type ?u.347556
α : Type u_1
β : Type ?u.347562
γ : Type ?u.347565
ι : Type ?u.347568
κ : Type ?u.347571
inst✝ : LinearOrder α
s✝ : Finset α
H : Finset.Nonempty s✝
x : α
s : Finset αᵒᵈ
⊢ WithBot.map (↑ofDual) (Finset.max s) = Finset.min (image (↑ofDual) s)
rw [min_eq_inf_withTop, inf_image]
no goals
F : Type ?u.347556
α : Type u_1
β : Type ?u.347562
γ : Type ?u.347565
ι : Type ?u.347568
κ : Type ?u.347571
inst✝ : LinearOrder α
s✝ : Finset α
H : Finset.Nonempty s✝
x : α
s : Finset αᵒᵈ
⊢ WithBot.map (↑ofDual) (Finset.max s) = inf s (WithTop.some ∘ ↑ofDual)
exact congr_fun Option.map_id _