proposition: Lemma lower_solution' : forall A n, tele (x' : A) (n' : nat) (v : vector A n') in (S n' = S n) <~> tele (x : A) in vector A n.
proof: Proof. intros A n. unshelve refine {| equiv a := _ |}. refine &(a.1 & _). destruct a. destruct pr2. destruct pr2. simpl in pr3. noconf pr3. exact pr2. unshelve refine {| equiv_inv a := _ |}. refine &(a.1, n & _). refine &(a.2 & eq_refl). apply axiom. apply axiom. apply axiom. Defined.
imports: Equations DepElimDec EqDecInstances Utf8