diff --git a/lean-peano.cabal b/lean-peano.cabal
--- a/lean-peano.cabal
+++ b/lean-peano.cabal
@@ -1,14 +1,15 @@
-cabal-version: >= 1.12
+cabal-version: 1.12
 
 name:           lean-peano
-version:        1.0.1.0
-synopsis:       A maximally lazy, simple implementation of the Peano numbers with minimal dependencies
+version:        1.0.2.0
+synopsis:       A maximally lazy, simple implementation of the Peano numbers with minimal dependencies.
 description:    Please see the README on GitHub at <https://github.com/oisdk/lean-peano#readme>
 homepage:       https://github.com/oisdk/lean-peano#readme
 bug-reports:    https://github.com/oisdk/lean-peano/issues
 author:         Donnacha Oisín Kidney
 maintainer:     mail@doisinkidney.com
 copyright:      2020 Donnacha Oisín Kidney
+category:       Numeric
 license:        MIT
 license-file:   LICENSE
 build-type:     Custom
diff --git a/src/Numeric/Peano.hs b/src/Numeric/Peano.hs
--- a/src/Numeric/Peano.hs
+++ b/src/Numeric/Peano.hs
@@ -1,6 +1,6 @@
-{-# LANGUAGE BangPatterns         #-}
-{-# LANGUAGE DeriveDataTypeable   #-}
-{-# LANGUAGE DeriveGeneric        #-}
+{-# LANGUAGE BangPatterns       #-}
+{-# LANGUAGE DeriveDataTypeable #-}
+{-# LANGUAGE DeriveGeneric      #-}
 
 -- | Peano numerals. Effort is made to make them as efficient as
 -- possible, and as lazy as possible, but they are many orders of
@@ -31,12 +31,12 @@
 -- False
 module Numeric.Peano where
 
-import           Data.List                   (unfoldr)
+import           Data.List       (unfoldr)
 
-import           Control.DeepSeq             (NFData (rnf))
+import           Control.DeepSeq (NFData (rnf))
 
-import           Data.Data                   (Data, Typeable)
-import           GHC.Generics                (Generic)
+import           Data.Data       (Data, Typeable)
+import           GHC.Generics    (Generic)
 
 import           Numeric.Natural
 
@@ -84,7 +84,7 @@
 foldlNat' :: (a -> a) -> a -> Nat -> a
 foldlNat' f = go
   where
-    go !b Z = b
+    go !b Z     = b
     go !b (S n) = go (f b) n
 {-# INLINE foldlNat' #-}
 
@@ -96,8 +96,7 @@
     compare (S _) Z     = GT
 
     Z   <= _   = True
-    S _ <= Z   = False
-    S n <= S m = n <= m
+    S n <= m   = n < m
 
     _ < Z = False
     n < S m = n <= m
@@ -105,12 +104,12 @@
     (>=) = flip (<=)
     (>) = flip (<)
 
-    min Z _ = Z
-    min _ Z = Z
+    min Z _         = Z
+    min _ Z         = Z
     min (S n) (S m) = S (min n m)
 
-    max Z m = m
-    max n Z = n
+    max Z m         = m
+    max n Z         = n
     max (S n) (S m) = S (max n m)
 
 -- | Subtraction stops at zero.
@@ -120,7 +119,7 @@
     n + m = foldrNat S m n
     n * m = foldrNat (m+) Z n
     abs = id
-    signum Z = Z
+    signum Z     = Z
     signum (S _) = S Z
     fromInteger n
         | n < 0 = error "cannot convert negative integers to Peano numbers"
@@ -176,7 +175,7 @@
 instance Enum Nat where
     succ = S
     pred (S n) = n
-    pred Z = error "pred called on zero nat"
+    pred Z     = error "pred called on zero nat"
     fromEnum = foldlNat' succ 0
     toEnum m
       | m < 0 = error "cannot convert negative number to Peano"
@@ -187,22 +186,22 @@
     enumFrom = iterate S
     enumFromTo n m = unfoldr f (n, S m - n)
       where
-        f (_,Z) = Nothing
+        f (_,Z)   = Nothing
         f (e,S l) = Just (e, (S e, l))
     enumFromThen n m = iterate t n
       where
-        ts Z mm = (+) mm
+        ts Z mm          = (+) mm
         ts (S nn) (S mm) = ts nn mm
-        ts nn Z = subtract nn
+        ts nn Z          = subtract nn
         t = ts n m
     enumFromThenTo n m t = unfoldr f (n, jm)
       where
         ts (S nn) (S mm) = ts nn mm
-        ts Z mm = (S t - n, (+) mm, mm)
-        ts nn Z = (S n - t, subtract nn, nn)
+        ts Z mm          = (S t - n, (+) mm, mm)
+        ts nn Z          = (S n - t, subtract nn, nn)
         (jm,tf,tt) = ts n m
         td = subtract tt
-        f (_,Z) = Nothing
+        f (_,Z)       = Nothing
         f (e,l@(S _)) = Just (e, (tf e, td l))
 
 
diff --git a/src/Numeric/Peano/Typelevel.hs b/src/Numeric/Peano/Typelevel.hs
--- a/src/Numeric/Peano/Typelevel.hs
+++ b/src/Numeric/Peano/Typelevel.hs
@@ -54,13 +54,12 @@
 
 -- | '<=' on type-level naturals.
 type family (<=) (n :: Nat) (m :: Nat) :: Bool where
-    Z   <= _   = True
-    S _ <= Z   = False
-    S n <= S m = n <= m
+    Z   <= _ = True
+    S n <= m = n < m
 
 -- | '<' on type-level naturals.
 type family (<) (n :: Nat) (m :: Nat) :: Bool where
-    _ < Z = False
+    _ < Z   = False
     n < S m = n <= m
 
 -- | The minimum of two type-level naturals.