proposition: Lemma fraction_encoding_equal : forall (m n : Z) (Hn1 Hn2 : n <> 0%Z), fraction_encoding m n Hn1 = fraction_encoding m n Hn2.
proof: Proof. intros m n Hn1. unfold fraction_encoding at 2; fold fraction_encoding. functional induction (fraction_encoding m n Hn1); intros Hn2. - rewrite e; f_equal; apply positive_fraction_encoding_equal. - rewrite e; f_equal; apply positive_fraction_encoding_equal. - rewrite e0; trivial. Defined.
imports: Coq(FunInd)