case intro
ι : Type ?u.344295
α : Type u
β : Type v
γ : Type w
δ : Type x
l₁ l₂ : List α
f✝ f g : α → Option α
a : α
l : List α
H : ∀ (a_1 : α), a_1 ∈ a :: l → f a_1 = g a_1
H₁ : f a = g a
H₂ : ∀ (x : α), x ∈ l → f x = g x
⊢ lookmap f (a :: l) = lookmap g (a :: l)
ι : Type ?u.344295
α : Type u
β : Type v
γ : Type w
δ : Type x
l₁ l₂ : List α
f✝ f g : α → Option α
a : α
l : List α
H : ∀ (a_1 : α), a_1 ∈ a :: l → f a_1 = g a_1
⊢ lookmap f (a :: l) = lookmap g (a :: l)
cases' forall_mem_cons.1 H with H₁ H₂
case intro.none
ι : Type ?u.344295
α : Type u
β : Type v
γ : Type w
δ : Type x
l₁ l₂ : List α
f✝ f g : α → Option α
a : α
l : List α
H : ∀ (a_1 : α), a_1 ∈ a :: l → f a_1 = g a_1
H₁ : f a = g a
H₂ : ∀ (x : α), x ∈ l → f x = g x
h : g a = none
⊢ lookmap f (a :: l) = lookmap g (a :: l)

case intro.some
ι : Type ?u.344295
α : Type u
β : Type v
γ : Type w
δ : Type x
l₁ l₂ : List α
f✝ f g : α → Option α
a : α
l : List α
H : ∀ (a_1 : α), a_1 ∈ a :: l → f a_1 = g a_1
H₁ : f a = g a
H₂ : ∀ (x : α), x ∈ l → f x = g x
b : α
h : g a = some b
⊢ lookmap f (a :: l) = lookmap g (a :: l)
case intro
ι : Type ?u.344295
α : Type u
β : Type v
γ : Type w
δ : Type x
l₁ l₂ : List α
f✝ f g : α → Option α
a : α
l : List α
H : ∀ (a_1 : α), a_1 ∈ a :: l → f a_1 = g a_1
H₁ : f a = g a
H₂ : ∀ (x : α), x ∈ l → f x = g x
⊢ lookmap f (a :: l) = lookmap g (a :: l)
cases' h : g a with b
no goals
case intro.none
ι : Type ?u.344295
α : Type u
β : Type v
γ : Type w
δ : Type x
l₁ l₂ : List α
f✝ f g : α → Option α
a : α
l : List α
H : ∀ (a_1 : α), a_1 ∈ a :: l → f a_1 = g a_1
H₁ : f a = g a
H₂ : ∀ (x : α), x ∈ l → f x = g x
h : g a = none
⊢ lookmap f (a :: l) = lookmap g (a :: l)
simp [h, H₁.trans h, lookmap_congr H₂]
no goals
case intro.some
ι : Type ?u.344295
α : Type u
β : Type v
γ : Type w
δ : Type x
l₁ l₂ : List α
f✝ f g : α → Option α
a : α
l : List α
H : ∀ (a_1 : α), a_1 ∈ a :: l → f a_1 = g a_1
H₁ : f a = g a
H₂ : ∀ (x : α), x ∈ l → f x = g x
b : α
h : g a = some b
⊢ lookmap f (a :: l) = lookmap g (a :: l)
simp [lookmap_cons_some _ _ h, lookmap_cons_some _ _ (H₁.trans h)]