import data.examples.vector data.prod open nat vector prod variables {A B : Type} definition unzip : Π {n}, vector (A × B) n → vector A n × vector B n | unzip nil := (nil, nil) | unzip ((a, b) :: t) := (a :: pr₁ (unzip t), b :: pr₂ (unzip t)) theorem unzip_nil : unzip nil = (@nil A, @nil B) := rfl theorem unzip_cons {n : nat} (a : A) (b : B) (t : vector (A × B) n) : unzip ((a, b) :: t) = (a :: pr₁ (unzip t), b :: pr₂ (unzip t)) := rfl