diff --git a/Language/Nock5K/Spec.hs b/Language/Nock5K/Spec.hs
index 1102368..9d1bd0a 100644
--- a/Language/Nock5K/Spec.hs
+++ b/Language/Nock5K/Spec.hs
@@ -57,14 +57,12 @@ tis a                    = Left "=a"
   \/[(a + a + 1) b]  \/[3 \/[a b]]
   \/a                \/a
 @-}
-fas (Atom 1 :- a)                            = return a
-fas (Atom 2 :- a :- b)                       = return a
-fas (Atom 3 :- a :- b)                       = return b
-fas (Atom a :- b) | a > 2 && a `mod` 2 == 0  = do x <- fas $ Atom (a `div` 2) :- b
-                                                  fas $ Atom 2 :- x
-fas (Atom a :- b) | a > 3 && a `mod` 2 == 1  = do x <- fas $ Atom (a `div` 2) :- b
-                                                  fas $ Atom 3 :- x
-fas a                                        = Left "/a"
+fas (Atom 1 :- a)          = return a
+fas (Atom 2 :- a :- b)     = return a
+fas (Atom 3 :- a :- b)     = return b
+fas (Atom a :- b) | a > 3  = do  x <- fas $ Atom (a `div` 2) :- b
+                                 fas $ Atom (2 + (a `mod` 2)) :- x
+fas a                      = Left "/a"
 
 {-|@
   \*[a [b c] d]      [\*[a b c] \*[a d]]
diff --git a/test.hs b/test.hs
index 9dacdea..0bf906a 100644
--- a/test.hs
+++ b/test.hs
@@ -34,6 +34,12 @@ prop_6_is_if a' b = nock (ifs $ Atom 0) == Right (Atom (a + 1)) && nock (ifs $ A
     ifs c = Atom a :- Atom 6 :- (Atom 1 :- c) :- (Atom 4 :- Atom 0 :- Atom 1) :- (Atom 1 :- b)
     a = abs a'
 
+prop_fas_induct a' b = fas (a + a) b == fasmn 2 a b && fas (a + a + 1) b == fasmn 3 a b
+  where fas c d = nock $ d :- Atom c
+        fasmn m n c = do x <- fas n c
+                         fas m x
+        a = abs a'
+
 test_hint_crash = assert $ nock bad == Left "/a"
   where bad = pn "[42 10 [0 0 2] 0 1]"
 
@@ -43,6 +49,7 @@ test_eval_strict = assert $ nock bad == Left "/a"
 tests = [ testProperty "parse.show"    prop_parse_show
         , testProperty "decrement"     prop_dec
         , testProperty "6_is_if"       prop_6_is_if
+        , testProperty "fas_induct"    prop_fas_induct
         , testCase     "10_hint_crash" test_hint_crash
         , testCase     "eval_strict"   test_eval_strict
         ]