proposition: Theorem slope_cmp₂ : ∀ pt₁ pt₂ pt₃, fst pt₁ < fst pt₂ < fst pt₃ → (slope_expr pt₁ pt₃ ?= slope_expr pt₁ pt₂) = (slope_expr pt₂ pt₃ ?= slope_expr pt₁ pt₃).
proof: Proof. intros (x₁, y₁) (x₂, y₂) (x₃, y₃) (Hlt₁, Hlt₂). assert (x₁ < x₃) as Hlt₃ by (eapply Qlt_trans; eassumption). rewrite slope_cmp_norm₁₃₁₂; [ idtac | split; assumption ]. rewrite slope_cmp_norm₂₃₁₃; [ idtac | split; assumption ]. reflexivity. Qed.
imports: Utf8 QArith Slope_base Misc