(n : nat) : binnat := match n with | O => bzero | S n' => Succ ( n') end. End basics. Section binary_equiv. Local unary' (n : binnat) : nat := match n with | bzero => O | double1 n' => Double1 (unary' n') | double2 n' => Double2 (unary' n') end. Local Definition succunary (n : binnat) : unary' (Succ n) = S (unary' n). Proof. induction n. - reflexivity. - reflexivity. - simpl. rewrite IHn. reflexivity. Qed.
Require Import Require Import Require Import