diff --git a/crates/types/src/compound/peano.rs b/crates/types/src/compound/peano.rs
index 83a199e..d3825e4 100644
--- a/crates/types/src/compound/peano.rs
+++ b/crates/types/src/compound/peano.rs
@@ -2,14 +2,20 @@ pub struct PNext<P>(P);
 pub struct P0;
 pub type P1 = PNext<P0>;
 
-pub trait Peano { }
+pub trait Peano {
+    type Next: PeanoNonZero;
+}
 
 pub trait PeanoNonZero {
     type Prev: Peano;
 }
 
-impl Peano for P0 { }
-impl<P: Peano> Peano for PNext<P> {}
+impl Peano for P0 {
+    type Next = P1;
+}
+impl<P: Peano> Peano for PNext<P> {
+    type Next = PNext<PNext<P>>;
+}
 impl<P: Peano> PeanoNonZero for PNext<P> {
     type Prev = P;
 }