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

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

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