rename_i prop₁ _ _ _ _ _ _ _ _ _ prop₄ _ _ _
case h_2.inr
n : ℕ
v₁ v₂ v₃ : Variables n order.Lex
m : ℕ
a b c : Variables m order.Lex
property✝⁴ property✝³ property✝² : List.length [] = m
h : Order.lex_impl { val := [], property := property✝⁴ } { val := [], property := property✝³ }
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 :
  Variables.mul { val := [], property := property✝⁴ } { val := [], property := property✝² } =
    { val := x✝ :: tail✝¹, property := property✝¹ }
heq✝ :
  Variables.mul { val := [], property := property✝³ } { val := [], property := property✝² } =
    { val := y✝ :: tail✝, property := property✝ }
h✝ : ¬x✝ = y✝
⊢ x✝ ≤ y✝
case h_2.inr
n : ℕ
v₁ v₂ v₃ : Variables n order.Lex
m : ℕ
a b c : Variables m order.Lex
prop₁ property✝² property✝¹ : List.length [] = m
h : Order.lex_impl { val := [], property := prop₁ } { val := [], property := property✝² }
v₁✝ v₂✝ : Vector ℕ m
x✝ : ℕ
tail✝¹ : List ℕ
property✝ : List.length (x✝ :: tail✝¹) = m
y✝ : ℕ
tail✝ : List ℕ
prop₄ : List.length (y✝ :: tail✝) = m
heq✝¹ :
  Variables.mul { val := [], property := prop₁ } { val := [], property := property✝¹ } =
    { val := x✝ :: tail✝¹, property := property✝ }
heq✝ :
  Variables.mul { val := [], property := property✝² } { val := [], property := property✝¹ } =
    { val := y✝ :: tail✝, property := prop₄ }
h✝ : ¬x✝ = y✝
⊢ x✝ ≤ y✝