proposition: Theorem slope_cmp_norm₁₃₁₂ : ∀ x₁ y₁ x₂ y₂ x₃ y₃, x₁ < x₂ < x₃ → (slope_expr (x₁, y₁) (x₃, y₃) ?= slope_expr (x₁, y₁) (x₂, y₂)) = (x₁ * y₂ + x₂ * y₃ + x₃ * y₁ ?= x₁ * y₃ + x₂ * y₁ + x₃ * y₂).
proof: Proof. intros; apply Qcmp_sym, slope_cmp_norm₁₂₁₃; assumption. Qed.
imports: Utf8 QArith Slope_base Misc