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