rw [Order.lex_impl]
n : ℕ
v₁ v₂ v₃ : Variables n order.Lex
h₁ : Order.lex v₁ v₂
h₂ : Order.lex v₂ v₃
m : ℕ
a b c : Variables m order.Lex
x : ℕ
xs : List ℕ
p : List.length (x :: xs) = m
y : ℕ
ys : List ℕ
q : List.length (y :: ys) = m
z : ℕ
zs : List ℕ
l : List.length (z :: zs) = m
ab : Order.lex_impl { val := x :: xs, property := p } { val := y :: ys, property := q }
bc : Order.lex_impl { val := y :: ys, property := q } { val := z :: zs, property := l }
⊢ Order.lex_impl { val := x :: xs, property := p } { val := z :: zs, property := l }
n : ℕ
v₁ v₂ v₃ : Variables n order.Lex
h₁ : Order.lex v₁ v₂
h₂ : Order.lex v₂ v₃
m : ℕ
a b c : Variables m order.Lex
x : ℕ
xs : List ℕ
p : List.length (x :: xs) = m
y : ℕ
ys : List ℕ
q : List.length (y :: ys) = m
z : ℕ
zs : List ℕ
l : List.length (z :: zs) = m
ab : Order.lex_impl { val := x :: xs, property := p } { val := y :: ys, property := q }
bc : Order.lex_impl { val := y :: ys, property := q } { val := z :: zs, property := l }
⊢ match { val := x :: xs, property := p }, { val := z :: zs, property := l } with
  | { val := [], property := property }, { val := [], property := property_1 } => True
  | { val := x_1 :: tail, property := property }, { val := y :: tail_1, property := property_1 } =>
    if x_1 = y then
      Order.lex_impl (Vector.tail { val := x :: xs, property := p }) (Vector.tail { val := z :: zs, property := l })
    else x_1 ≤ y