22 lines
757 B
Text
22 lines
757 B
Text
prelude
|
||
import Init.MetaTypes
|
||
import Init.Data.List.Basic
|
||
|
||
@[simp] theorem map_comp_map (f : α → β) (g : β → γ) : List.map g ∘ List.map f = List.map (g ∘ f) :=
|
||
sorry
|
||
|
||
theorem map_map (f : α → β) (g : β → γ) (xs : List α) : (xs.map f |>.map g) = xs.map (g ∘ f) :=
|
||
sorry
|
||
|
||
theorem ex1 (f : Nat → Nat) (xs : List Nat) : (xs.map f |>.map f) = xs.map (f ∘ f) := by
|
||
fail_if_success simp
|
||
simp [map_map]
|
||
done
|
||
|
||
theorem ex2 (f : Nat → Nat) : List.map f ∘ List.map f ∘ List.map f = List.map (f ∘ f ∘ f) := by
|
||
simp
|
||
|
||
attribute [simp] map_map
|
||
|
||
theorem ex3 (f : Nat → Nat) (xs : List Nat) : (xs.map f |>.map f |>.map f) = xs.map (fun x => f (f (f x))) := by
|
||
simp (config := { unfoldPartialApp := true }) [Function.comp]
|