repeat contradiction
case inr.inl.inl.inl
n✝ : ℕ
v₁ v₂ : Variables n✝ order.GrLex
h✝³ : ¬Order.grlex.elem_sum v₁ < Order.grlex.elem_sum v₂
h✝² : Order.grlex.elem_sum v₁ = Order.grlex.elem_sum v₂
h✝¹ : algebra.Order.bgrlex.elem_sum v₁ = algebra.Order.bgrlex.elem_sum v₂
h✝ : Order.lex v₁ v₂
h : True
a✝ : algebra.Order.bgrlex.elem_sum v₂ ≤ algebra.Order.bgrlex.elem_sum v₁
hh : ¬Order.lex v₁ v₂
⊢ False

case inr.inl.inl.inr
n✝ : ℕ
v₁ v₂ : Variables n✝ order.GrLex
h✝³ : ¬Order.grlex.elem_sum v₁ < Order.grlex.elem_sum v₂
h✝² : Order.grlex.elem_sum v₁ = Order.grlex.elem_sum v₂
h✝¹ : algebra.Order.bgrlex.elem_sum v₁ = algebra.Order.bgrlex.elem_sum v₂
h✝ : ¬Order.lex v₁ v₂
h : False
⊢ algebra.Order.bgrlex.elem_sum v₂ ≤ algebra.Order.bgrlex.elem_sum v₁ → ¬Order.lex v₁ v₂ → False

case inr.inl.inr
n✝ : ℕ
v₁ v₂ : Variables n✝ order.GrLex
h✝² : ¬Order.grlex.elem_sum v₁ < Order.grlex.elem_sum v₂
h✝¹ : Order.grlex.elem_sum v₁ = Order.grlex.elem_sum v₂
h : if Order.lex v₁ v₂ then True else False
h✝ : ¬algebra.Order.bgrlex.elem_sum v₁ = algebra.Order.bgrlex.elem_sum v₂
⊢ algebra.Order.bgrlex.elem_sum v₂ ≤ algebra.Order.bgrlex.elem_sum v₁ → False

case inr.inr
n✝ : ℕ
v₁ v₂ : Variables n✝ order.GrLex
h✝¹ : ¬Order.grlex.elem_sum v₁ < Order.grlex.elem_sum v₂
h✝ : ¬Order.grlex.elem_sum v₁ = Order.grlex.elem_sum v₂
h : False
⊢ algebra.Order.bgrlex v₁ v₂ = true
no goals