α✝ : Type u
β : Type v
γ : Type w
α : Type u
inst✝ : AddMonoid α
as : List α
⊢ map (fun x => default + x) as = as
α✝ : Type u
β : Type v
γ : Type w
α : Type u
inst✝ : AddMonoid α
as : List α
⊢ add [] as = as
rw [add, @nil_pointwise α α α ⟨0⟩ ⟨0⟩]
α✝ : Type u
β : Type v
γ : Type w
α : Type u
inst✝ : AddMonoid α
as : List α
⊢ map (fun x => default + x) as = map id as
α✝ : Type u
β : Type v
γ : Type w
α : Type u
inst✝ : AddMonoid α
as : List α
⊢ map (fun x => default + x) as = as
apply Eq.trans _ (map_id as)
case e_f.h
α✝ : Type u
β : Type v
γ : Type w
α : Type u
inst✝ : AddMonoid α
as : List α
x : α
⊢ default + x = id x
α✝ : Type u
β : Type v
γ : Type w
α : Type u
inst✝ : AddMonoid α
as : List α
⊢ map (fun x => default + x) as = map id as
congr with x
no goals
case e_f.h
α✝ : Type u
β : Type v
γ : Type w
α : Type u
inst✝ : AddMonoid α
as : List α
x : α
⊢ default + x = id x
exact zero_add x