proposition: Lemma seq_of_max_is_increasing : ∀ g : ℕ → ℕ, is_increasing (seq_of_max g).
proof: Proof. Take g : (ℕ → ℕ). We need to show that (for all k : ℕ, (seq_of_max g k ≤ seq_of_max g (S k))%nat). Take k : ℕ. We need to show that (seq_of_max g k ≤ Nat.max (g (S k)) (seq_of_max g k))%nat. We conclude that (seq_of_max g k ≤ Nat.max (g (S k)) (seq_of_max g k))%nat. Qed.
imports: Coq.Reals.Reals ZArith Lra Classical Classical_Pred_Type ClassicalChoice Automation Libs.Negation Notations Tactics Waterprove