21 lines
498 B
Text
21 lines
498 B
Text
|
||
|
||
inductive Vec.{u} (α : Type u) : Nat → Type u
|
||
| nil : Vec α 0
|
||
| cons : α → {n : Nat} → Vec α n → Vec α (n+1)
|
||
|
||
open Vec
|
||
universes u
|
||
|
||
variables {α : Type u}
|
||
variables (f : α → α → α)
|
||
|
||
def mapHead1 : {n : Nat} → Vec α n → Vec α n → Vec α n
|
||
| _, nil, nil => nil
|
||
| _, cons a va, cons b bv => cons (f a b) va
|
||
|
||
theorem ex1 : mapHead1 f nil nil = nil :=
|
||
rfl
|
||
|
||
theorem ex2 (a b : α) (n : Nat) (va vb : Vec α n) : mapHead1 f (cons a va) (cons b vb) = cons (f a b) va :=
|
||
rfl
|