split
n✝ : ℕ
v₁ v₂ : Vector ℕ n✝
h✝ : lex_impl v₁ v₂
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 : lex_impl { val := x :: xs, property := property✝¹ } { val := y :: ys, property := property✝ }
⊢ (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) = true then
        algebra.Order.ble_lex_impl (Vector.tail { val := x :: xs, property := property✝¹ })
          (Vector.tail { val := y :: ys, property := property✝ })
      else decide (x_1 ≤ y_1)) =
    true
case h_1
n✝ : ℕ
v₁ v₂ : Vector ℕ n✝
h✝ : lex_impl v₁ v₂
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 : lex_impl { val := x :: xs, property := property✝³ } { val := y :: ys, property := property✝² }
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 = true

case h_2
n✝ : ℕ
v₁ v₂ : Vector ℕ n✝
h✝ : lex_impl v₁ v₂
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 : lex_impl { val := x :: xs, property := property✝³ } { val := y :: ys, property := property✝² }
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✝) = true then
      algebra.Order.ble_lex_impl (tail { val := x :: xs, property := property✝³ })
        (tail { val := y :: ys, property := property✝² })
    else decide (x✝ ≤ y✝)) =
    true