diff --git a/src/Verifier/SAW/Rewriter.hs b/src/Verifier/SAW/Rewriter.hs
index 48b50a7c..1479e090 100644
--- a/src/Verifier/SAW/Rewriter.hs
+++ b/src/Verifier/SAW/Rewriter.hs
@@ -60,6 +60,7 @@ import Data.Foldable (Foldable)
 import Control.Lens
 import Control.Monad.Identity
 import Control.Monad.State
+import Control.Monad.Trans.Maybe
 import Data.Bits
 import qualified Data.Foldable as Foldable
 import Data.IORef (IORef)
@@ -119,6 +120,32 @@ first_order_match pat term = match pat term Map.empty
 -- occur as the 2nd argument of an @App@ constructor. This ensures
 -- that instantiations are well-typed.
 
+-- | An enhanced matcher that can handle some patterns containing lambdas.
+scMatch :: forall s. SharedContext s -> SharedTerm s -> SharedTerm s -> MaybeT IO (Map DeBruijnIndex (SharedTerm s))
+scMatch sc pat term = match 0 pat term Map.empty
+  where
+    match :: Int -> SharedTerm s -> SharedTerm s -> Map DeBruijnIndex (SharedTerm s) -> MaybeT IO (Map DeBruijnIndex (SharedTerm s))
+    match depth x y m =
+      case (unwrapTermF x, unwrapTermF y) of
+        -- check that neither x nor y contains bound variables less than `depth`
+        (LocalVar i, _) | i >= depth && looseVars y .&. (bit depth - 1) == 0 ->
+          do -- decrement loose variables in y by `depth`
+             y1 <- lift $ S.instantiateVarList sc 0 (replicate depth (error "scMatch: impossible")) y
+             let (my2, m') = insertLookup (i - depth) y1 m
+             case my2 of
+               Nothing -> return m'
+               Just y2 -> if y == y2 then return m' else mzero
+        (App x1 x2, App y1 y2) ->
+          match depth x1 y1 m >>= match depth x2 y2
+        (FTermF xf, FTermF yf) ->
+          case zipWithFlatTermF (match depth) xf yf of
+            Nothing -> mzero
+            Just zf -> Foldable.foldl (>=>) return zf m
+        (Lambda _ t1 x1, Lambda _ t2 x2) ->
+          match depth t1 t2 m >>= match (depth + 1) x1 x2
+        (_, _) ->
+          if x == y then return m else mzero
+
 ----------------------------------------------------------------------
 -- Building rewrite rules
 
@@ -356,8 +383,9 @@ rewriteSharedTerm sc ss t0 =
              [Either (RewriteRule (SharedTerm s)) (Conversion (SharedTerm s))] ->
              SharedTerm s -> IO (SharedTerm s)
     apply [] t = return t
-    apply (Left (RewriteRule {lhs, rhs}) : rules) t =
-      case first_order_match lhs t of
+    apply (Left (RewriteRule {lhs, rhs}) : rules) t = do
+      result <- runMaybeT (scMatch sc lhs t)
+      case result of
         Nothing -> apply rules t
         Just inst
           | lhs == rhs ->