proposition: Lemma dist_refl : forall n : nat, dist (n,n) = 0.
proof: Proof. intro n. unfold dist. simpl. rewrite sub_diag. simpl. reflexivity. Qed.
imports: Coq.Logic.ClassicalEpsilon ClassicalFacts PropExtensionalityFacts Lia PeanoNat ProofIrrelevance ExtensionalityFacts List Coq.Strings.Ascii