proposition: Lemma double_is_even : forall n : nat, Nat.even (2 * n) = true.
proof: Proof. Take n : nat. It holds that (Nat.even (2 * n) = Nat.even (0 + 2 * n)). It suffices to show that (Nat.even (0 + 2*n) = true). By Nat.even_add_mul_2 it holds that (Nat.even (0 + 2*n) = Nat.even 0). It holds that (Nat.even 0 = true). We conclude that (Nat.even (0 + 2 * n) = true). Qed.
imports: Coq.Reals.Reals Automation Libs.Analysis.MetricSpaces Libs.Analysis.SequencesMetric Notations Tactics