diff --git a/src/main.rs b/src/main.rs
index 7772fd0..3589ed4 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -47,7 +47,7 @@ impl Incrementable for AtomSet {
 }
 
 #[derive(Debug, Default)]
-struct Lattice<I: Incrementable + Default, Ext = ()> {
+struct Lattice<I: Incrementable + Default, Ext> {
     ext: Ext,
     order: Vec<I>,
 }
@@ -58,7 +58,7 @@ trait LatticeAbstract {
     fn is_lattice(&self) -> bool;
 }
 
-impl Display for Lattice<Atom> {
+impl Display for Lattice<Atom, ()> {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         for (i, atom) in self.order.iter().enumerate() {
             let s = atom
@@ -72,7 +72,7 @@ impl Display for Lattice<Atom> {
     }
 }
 
-impl<I: Incrementable + Default> Incrementable for Lattice<I> {
+impl<I: Incrementable + Default, Ext> Incrementable for Lattice<I, Ext> {
     fn increment(&mut self) -> IncrementResult {
         for atom in &mut self.order {
             if let Good = atom.increment() {
@@ -83,7 +83,7 @@ impl<I: Incrementable + Default> Incrementable for Lattice<I> {
     }
 }
 
-impl<I: Incrementable + Default> Lattice<I>
+impl<I: Incrementable + Default, Ext> Lattice<I, Ext>
 where
     Self: LatticeAbstract,
 {
@@ -140,29 +140,32 @@ where
         }
         return true;
     }
-    fn monotone<Inc, Ext>(&self, other: &Lattice<Inc, Ext>) -> bool
+    fn monotone<IncB, ExtB>(&self, other: &Lattice<IncB, ExtB>) -> bool
     where
-        Inc: Incrementable + Default,
-        Lattice<Inc, Ext>: LatticeAbstract,
+        IncB: Incrementable + Default,
+        Lattice<IncB, ExtB>: LatticeAbstract,
     {
         assert_eq!(self.order.len(), other.order.len());
-        for (a, b) in (0..self.order.len()).cartesian_product((0..other.order.len())) {
+        for (a, b) in (0..self.order.len()).cartesian_product(0..other.order.len()) {
             if self.le(a, b) && !other.le(a, b) {
                 return false;
             }
         }
         return true;
     }
-    fn equal<Inc, Ext>(&self, other: &Lattice<Inc, Ext>) -> bool
+    fn equal<IncB, ExtB>(&self, other: &Lattice<IncB, ExtB>) -> bool
     where
-        Inc: Incrementable + Default,
-        Lattice<Inc, Ext>: LatticeAbstract,
+        IncB: Incrementable + Default,
+        Lattice<IncB, ExtB>: LatticeAbstract,
     {
         self.monotone(other) && other.monotone(self)
     }
 }
 
-impl Lattice<Atom> {
+impl Lattice<Atom, ()> {
+    fn new() -> Self {
+        Self::default()
+    }
     fn is_transitive(&self) -> bool {
         for (i, j) in (0..self.order.len()).cartesian_product(0..self.order.len()) {
             if !self.le(i, j) && self.le_transitive(i, j) {
@@ -185,7 +188,7 @@ impl Lattice<Atom> {
     }
 }
 
-impl LatticeAbstract for Lattice<Atom> {
+impl LatticeAbstract for Lattice<Atom, ()> {
     fn le(&self, a: usize, b: usize) -> bool {
         if a == b {
             return true;
@@ -212,17 +215,8 @@ impl LatticeAbstract for Lattice<Atom> {
     }
 }
 
-fn main() {
-    let mut lattice = Lattice::default();
-    for (i, _) in repeat(0).enumerate() {
-        print!("{}", lattice);
-        println!("iteration {}", i);
-        lattice.next_lattice();
-    }
-}
-
 #[cfg(test)]
-mod tests {
+mod lattice_tests {
     use super::*;
     use std::error::Error;
 
@@ -292,10 +286,9 @@ mod tests {
     }
 }
 
-
 struct Mapping<'a> {
-    domain: &'a Lattice<Atom>,
-    image: &'a Lattice<Atom>,
+    domain: &'a Lattice<Atom, ()>,
+    image: &'a Lattice<Atom, ()>,
 }
 
 // function: Lattice<AtomSet>,
@@ -303,7 +296,7 @@ struct Mapping<'a> {
 type Operator<'a> = Lattice<AtomSet, Mapping<'a>>;
 
 impl<'a> Operator<'a> {
-    fn new(domain: &'a Lattice<Atom>, image: &'a Lattice<Atom>) -> Operator<'a> {
+    fn new(domain: &'a Lattice<Atom, ()>, image: &'a Lattice<Atom, ()>) -> Operator<'a> {
         Lattice {
             ext: Mapping { domain, image },
             order: vec![AtomSet { included: vec![] }; image.order.len()],
@@ -344,6 +337,54 @@ impl<'a> LatticeAbstract for Operator<'a> {
     }
 
     fn is_lattice(&self) -> bool {
-        self.all_nonempty() && self.ext.image.equal()
+        self.all_nonempty() && self.ext.image.equal(self)
+    }
+}
+
+impl<'a> Display for Operator<'a> {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        for (i, atom) in self.order.iter().enumerate() {
+            let s = atom
+                .included
+                .iter()
+                .map(|&b| if b { "1 " } else { "0 " })
+                .collect::<String>();
+            writeln!(f, "{}: {}", i, s)?;
+        }
+        Ok(())
+    }
+}
+
+#[cfg(test)]
+mod operator_tests {
+    use super::*;
+    use std::error::Error;
+
+    #[test]
+    fn test_operator() {
+    }
+}
+
+fn main() {
+    let mut domain = Lattice::<Atom, ()>::new();
+    let image = Lattice {
+        ext: (),
+        order: vec![
+            Atom { smaller: vec![] },
+            Atom {
+                smaller: vec![true],
+            },
+            Atom {
+                smaller: vec![true, false],
+            },
+        ],
+    };
+    loop {
+        domain.next_lattice();
+        println!("{}", domain);
+        let mut operator = Operator::new(&domain, &image);
+        while let Good = operator.next_lattice() {
+            println!("{}", operator);
+        }
     }
 }