∀ (ctx : Nat.Linear.Context) (a b c d : Nat.Linear.Expr),
  a.inc.toNormPoly.cancel b.toNormPoly = (c.inc.toPoly, d.toPoly) →
    (Nat.Linear.Expr.denote ctx a < Nat.Linear.Expr.denote ctx b) =
      (Nat.Linear.Expr.denote ctx c < Nat.Linear.Expr.denote ctx d)