diff --git a/src/main.rs b/src/main.rs
index f671a4d..7772fd0 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -12,14 +12,9 @@ trait Incrementable {
     fn increment(&mut self) -> IncrementResult;
 }
 
-#[derive(Debug, Default, Clone)]
-struct Atom {
-    smaller: Vec<bool>,
-}
-
-impl Incrementable for Atom {
+impl Incrementable for Vec<bool> {
     fn increment(&mut self) -> IncrementResult {
-        for a in &mut self.smaller {
+        for a in self {
             *a = !*a;
             if *a {
                 return Good;
@@ -29,14 +24,38 @@ impl Incrementable for Atom {
     }
 }
 
+#[derive(Debug, Default, Clone)]
+struct Atom {
+    smaller: Vec<bool>,
+}
+
+impl Incrementable for Atom {
+    fn increment(&mut self) -> IncrementResult {
+        self.smaller.increment()
+    }
+}
+
+#[derive(Debug, Default, Clone)]
+struct AtomSet {
+    included: Vec<bool>,
+}
+
+impl Incrementable for AtomSet {
+    fn increment(&mut self) -> IncrementResult {
+        self.included.increment()
+    }
+}
+
 #[derive(Debug, Default)]
-struct Lattice<I: Incrementable + Default> {
+struct Lattice<I: Incrementable + Default, Ext = ()> {
+    ext: Ext,
     order: Vec<I>,
 }
 
 trait LatticeAbstract {
     fn le(&self, a: usize, b: usize) -> bool;
-    fn grow(&mut self);
+    fn grow(&mut self) -> IncrementResult;
+    fn is_lattice(&self) -> bool;
 }
 
 impl Display for Lattice<Atom> {
@@ -64,41 +83,24 @@ impl<I: Incrementable + Default> Incrementable for Lattice<I> {
     }
 }
 
-impl<I: Incrementable> Lattice<I>
+impl<I: Incrementable + Default> Lattice<I>
 where
     Self: LatticeAbstract,
 {
-    fn next_lattice(&mut self) {
+    fn next_lattice(&mut self) -> IncrementResult {
         self.increment();
         while !self.is_lattice() {
             if let Overflow = self.increment() {
-                self.grow();
+                if let Overflow = self.grow() {
+                    return Overflow;
+                }
             }
         }
+        return Good;
     }
     fn ge(&self, a: usize, b: usize) -> bool {
         return self.le(b, a);
     }
-    // The underlying ordering might not be transitive, this makes it so
-    fn le_transitive(&self, a: usize, b: usize) -> bool {
-        if self.le(a, b) {
-            return true;
-        }
-        for (b, &active) in self.order[b].smaller.iter().enumerate() {
-            if active && self.le_transitive(a, b) {
-                return true;
-            }
-        }
-        return false;
-    }
-    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) {
-                return false;
-            }
-        }
-        return true;
-    }
     fn is_bounded<C, F>(&self, subset: &Vec<usize>, bound_candidates: C, rel: F) -> bool
     where
         C: Iterator<Item = usize>,
@@ -122,10 +124,7 @@ where
         return true;
     }
 
-    fn is_lattice(&self) -> bool {
-        if !self.is_transitive() {
-            return false;
-        }
+    fn has_lub_glb(&self) -> bool {
         // A top/bottom element are inherent as are partial order conditions.
         // Lattice condition can only fail if a set of elements have non comparable upper/lower bounds
         // Possible optimization: a lack of LUB might imply no GLB so may only need to check one of them
@@ -141,6 +140,49 @@ where
         }
         return true;
     }
+    fn monotone<Inc, Ext>(&self, other: &Lattice<Inc, Ext>) -> bool
+    where
+        Inc: Incrementable + Default,
+        Lattice<Inc, Ext>: LatticeAbstract,
+    {
+        assert_eq!(self.order.len(), 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
+    where
+        Inc: Incrementable + Default,
+        Lattice<Inc, Ext>: LatticeAbstract,
+    {
+        self.monotone(other) && other.monotone(self)
+    }
+}
+
+impl Lattice<Atom> {
+    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) {
+                return false;
+            }
+        }
+        return true;
+    }
+    // The underlying ordering might not be transitive, this makes it so
+    fn le_transitive(&self, a: usize, b: usize) -> bool {
+        if self.le(a, b) {
+            return true;
+        }
+        for (b, &active) in self.order[b].smaller.iter().enumerate() {
+            if active && self.le_transitive(a, b) {
+                return true;
+            }
+        }
+        return false;
+    }
 }
 
 impl LatticeAbstract for Lattice<Atom> {
@@ -156,13 +198,17 @@ impl LatticeAbstract for Lattice<Atom> {
         }
         return false;
     }
-    fn grow(&mut self) {
+    fn grow(&mut self) -> IncrementResult {
         self.order = vec![Default::default(); self.order.len() + 1];
         for (i, atom) in self.order.iter_mut().enumerate() {
             *atom = Atom {
                 smaller: vec![false; i],
             }
         }
+        return Good;
+    }
+    fn is_lattice(&self) -> bool {
+        self.is_transitive() && self.has_lub_glb()
     }
 }
 
@@ -183,6 +229,7 @@ mod tests {
     #[test]
     fn test_is_lattice() -> Result<(), Box<dyn Error>> {
         let lattice = Lattice {
+            ext: (),
             order: vec![
                 Atom { smaller: vec![] },
                 Atom {
@@ -195,6 +242,7 @@ mod tests {
         };
         assert!(lattice.is_lattice());
         let lattice = Lattice {
+            ext: (),
             order: vec![
                 Atom { smaller: vec![] },
                 Atom {
@@ -211,6 +259,7 @@ mod tests {
     #[test]
     fn test_is_not_lattice() -> Result<(), Box<dyn Error>> {
         let lattice = Lattice {
+            ext: (),
             order: vec![
                 Atom { smaller: vec![] },
                 Atom {
@@ -223,6 +272,7 @@ mod tests {
         };
         assert!(!lattice.is_transitive());
         let lattice = Lattice {
+            ext: (),
             order: vec![
                 Atom { smaller: vec![] },
                 Atom {
@@ -242,45 +292,58 @@ mod tests {
     }
 }
 
-// struct Operator<'a> {
-//     lattice: &'a Lattice,
-//     top: Vec<bool>,
-//     ul: Vec<bool>,
-//     ur: Vec<bool>,
-//     dl: Vec<bool>,
-//     dr: Vec<bool>,
-//     bot: Vec<bool>,
-// }
 
-// impl<'a> Operator<'a> {
-//     fn new(lattice: &'a Lattice) -> Self {
-//         Operator {
-//             lattice,
-//             top: vec![false; lattice.order.len()],
-//             ul: vec![false; lattice.order.len()],
-//             ur: vec![false; lattice.order.len()],
-//             dl: vec![false; lattice.order.len()],
-//             dr: vec![false; lattice.order.len()],
-//             bot: vec![false; lattice.order.len()],
-//         }
-//     }
-//     fn increment(&mut self) {
-//         let mut data = [
-//             &mut self.bot,
-//             &mut self.dr,
-//             &mut self.dl,
-//             &mut self.ur,
-//             &mut self.ul,
-//             &mut self.top,
-//         ];
-//         data[4][0] = false;
-//         for (i, el) in data.iter_mut().enumerate() {
-//             for a in el.iter_mut() {
-//                 *a = !*a;
-//                 if *a {
-//                     return;
-//                 }
-//             }
-//         }
-//     }
-// }
+struct Mapping<'a> {
+    domain: &'a Lattice<Atom>,
+    image: &'a Lattice<Atom>,
+}
+
+// function: Lattice<AtomSet>,
+
+type Operator<'a> = Lattice<AtomSet, Mapping<'a>>;
+
+impl<'a> 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()],
+        }
+    }
+    fn all_nonempty(&self) -> bool {
+        self.order.iter().all(|set| set.included.iter().any(|&x| x))
+    }
+    fn le_helper<I: Iterator<Item = usize> + Clone>(&self, a: I, b: I) -> bool {
+        b.clone()
+            .all(|right| a.clone().any(|left| self.ext.domain.le(left, right)))
+    }
+}
+
+impl<'a> LatticeAbstract for Operator<'a> {
+    fn le(&self, a: usize, b: usize) -> bool {
+        let pick = |which: usize| {
+            self.order[which]
+                .included
+                .iter()
+                .enumerate()
+                .filter_map(|(i, &included)| if included { Some(i) } else { None })
+        };
+        let left = pick(a);
+        let right = pick(b);
+
+        if !self.le_helper(left.clone(), right.clone()) {
+            return false;
+        }
+        if !self.le_helper(right, left) {
+            return false;
+        }
+        return true;
+    }
+
+    fn grow(&mut self) -> IncrementResult {
+        return Overflow;
+    }
+
+    fn is_lattice(&self) -> bool {
+        self.all_nonempty() && self.ext.image.equal()
+    }
+}