split
n✝ : ℕ
v₁ v₂ : Vector ℕ n✝
h✝ : algebra.Order.ble_lex_impl v₁ v₂ = true
m : ℕ
a b : Vector ℕ m
x : ℕ
xs : List ℕ
property✝¹ : List.length (x :: xs) = m
y : ℕ
ys : List ℕ
property✝ : List.length (y :: ys) = m
h :
  algebra.Order.ble_lex_impl { val := x :: xs, property := property✝¹ } { val := y :: ys, property := property✝ } = true
⊢ match { val := x :: xs, property := property✝¹ }, { val := y :: ys, property := property✝ } with
  | { val := [], property := property }, { val := [], property := property_1 } => True
  | { val := x_1 :: tail, property := property }, { val := y_1 :: tail_1, property := property_1 } =>
    if x_1 = y_1 then
      lex_impl (Vector.tail { val := x :: xs, property := property✝¹ })
        (Vector.tail { val := y :: ys, property := property✝ })
    else x_1 ≤ y_1
case h_1
n✝ : ℕ
v₁ v₂ : Vector ℕ n✝
h✝ : algebra.Order.ble_lex_impl v₁ v₂ = true
m : ℕ
a b : Vector ℕ m
x : ℕ
xs : List ℕ
property✝³ : List.length (x :: xs) = m
y : ℕ
ys : List ℕ
property✝² : List.length (y :: ys) = m
h :
  algebra.Order.ble_lex_impl { val := x :: xs, property := property✝³ } { val := y :: ys, property := property✝² } =
    true
v₁✝ v₂✝ : Vector ℕ m
property✝¹ property✝ : List.length [] = m
heq✝¹ : { val := x :: xs, property := property✝³ } = { val := [], property := property✝¹ }
heq✝ : { val := y :: ys, property := property✝² } = { val := [], property := property✝ }
⊢ True

case h_2
n✝ : ℕ
v₁ v₂ : Vector ℕ n✝
h✝ : algebra.Order.ble_lex_impl v₁ v₂ = true
m : ℕ
a b : Vector ℕ m
x : ℕ
xs : List ℕ
property✝³ : List.length (x :: xs) = m
y : ℕ
ys : List ℕ
property✝² : List.length (y :: ys) = m
h :
  algebra.Order.ble_lex_impl { val := x :: xs, property := property✝³ } { val := y :: ys, property := property✝² } =
    true
v₁✝ v₂✝ : Vector ℕ m
x✝ : ℕ
tail✝¹ : List ℕ
property✝¹ : List.length (x✝ :: tail✝¹) = m
y✝ : ℕ
tail✝ : List ℕ
property✝ : List.length (y✝ :: tail✝) = m
heq✝¹ : { val := x :: xs, property := property✝³ } = { val := x✝ :: tail✝¹, property := property✝¹ }
heq✝ : { val := y :: ys, property := property✝² } = { val := y✝ :: tail✝, property := property✝ }
⊢ if x✝ = y✝ then
    lex_impl (tail { val := x :: xs, property := property✝³ }) (tail { val := y :: ys, property := property✝² })
  else x✝ ≤ y✝