simp
case inl
n✝ : ℕ
v₁ v₂ : Variables n✝ order.GrLex
h : algebra.Order.bgrlex v₁ v₂ = true
h✝ : Order.grlex.elem_sum v₁ < Order.grlex.elem_sum v₂
⊢ True

case inr
n✝ : ℕ
v₁ v₂ : Variables n✝ order.GrLex
h : algebra.Order.bgrlex v₁ v₂ = true
h✝ : ¬Order.grlex.elem_sum v₁ < Order.grlex.elem_sum v₂
⊢ if Order.grlex.elem_sum v₁ = Order.grlex.elem_sum v₂ then if Order.lex v₁ v₂ then True else False else False
case inr
n✝ : ℕ
v₁ v₂ : Variables n✝ order.GrLex
h : algebra.Order.bgrlex v₁ v₂ = true
h✝ : ¬Order.grlex.elem_sum v₁ < Order.grlex.elem_sum v₂
⊢ if Order.grlex.elem_sum v₁ = Order.grlex.elem_sum v₂ then if Order.lex v₁ v₂ then True else False else False