proposition: Lemma bounded_by_lower_bound_propform : ∀ (A : ℝ → Prop) (m : ℝ) (b : ℝ), is_lower_bound A m ⇒ A b ⇒ m ≤ b.
proof: Proof. Take A : (ℝ → Prop). Take m : ℝ. Take b: ℝ. Assume that (is_lower_bound A m) (i). Assume that (A b) (ii). We conclude that (m ≤ b). Qed.
imports: Classical Classical_Pred_Type Coq.Reals.Reals Automation Notations Tactics