simp at *
case h_1
n : ℕ
a : Variables n order.Lex
m : ℕ
v : Variables m order.Lex
p : 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 := p } = { val := [], property := property✝ }
⊢ True

case h_2
n : ℕ
a : Variables n order.Lex
m : ℕ
v : Variables m order.Lex
p : 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 := p } = { val := y✝ :: tail✝, property := property✝ }
⊢ if x✝ = y✝ then Order.lex_impl (tail { val := [], property := p }) (tail { val := [], property := p }) else x✝ ≤ y✝
case h_2
n : ℕ
a : Variables n order.Lex
m : ℕ
v : Variables m order.Lex
p : 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 := p } = { val := y✝ :: tail✝, property := property✝ }
⊢ if x✝ = y✝ then Order.lex_impl (tail { val := [], property := p }) (tail { val := [], property := p }) else x✝ ≤ y✝