split
n : ℕ
v₁ v₂ : Variables n order.Lex
m : ℕ
a b : Vector ℕ m
p q : List.length [] = m
⊢ (match { val := [], property := p }, { val := [], property := q } with
    | { val := [], property := property }, { val := [], property := property_1 } => True
    | { val := x :: tail, property := property }, { val := y :: tail_1, property := property_1 } =>
      if x = y then Order.lex_impl (Vector.tail { val := [], property := p }) (Vector.tail { val := [], property := q })
      else x ≤ y) ∨
    match { val := [], property := p }, { val := [], property := q } with
    | { val := [], property := property }, { val := [], property := property_1 } => True
    | { val := x :: tail, property := property }, { val := y :: tail_1, property := property_1 } =>
      if x = y then Order.lex_impl (Vector.tail { val := [], property := p }) (Vector.tail { val := [], property := q })
      else x ≤ y
case h_1
n : ℕ
v₁ v₂ : Variables n order.Lex
m : ℕ
a b : Vector ℕ m
p q : List.length [] = m
v₁✝ v₂✝ : Vector ℕ m
property✝¹ property✝ : List.length [] = m
heq✝¹ : { val := [], property := p } = { val := [], property := property✝¹ }
heq✝ : { val := [], property := q } = { val := [], property := property✝ }
⊢ True ∨ True

case h_2
n : ℕ
v₁ v₂ : Variables n order.Lex
m : ℕ
a b : Vector ℕ m
p q : List.length [] = m
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 := [], property := p } = { val := x✝ :: tail✝¹, property := property✝¹ }
heq✝ : { val := [], property := q } = { val := y✝ :: tail✝, property := property✝ }
⊢ (if x✝ = y✝ then Order.lex_impl (tail { val := [], property := p }) (tail { val := [], property := q })
    else x✝ ≤ y✝) ∨
    if x✝ = y✝ then Order.lex_impl (tail { val := [], property := p }) (tail { val := [], property := q }) else x✝ ≤ y✝