diff --git a/src/Elab/Monad.hs b/src/Elab/Monad.hs
index eafe2a2..8e645da 100644
--- a/src/Elab/Monad.hs
+++ b/src/Elab/Monad.hs
@@ -159,4 +159,4 @@ throwElab = liftIO . throwIO
 
 incName :: Name -> Name -> Name
 incName (Bound x _) n = Bound x (getNameNum n + 1)
-incName (Defined x k) n = Defined x (getNameNum n + 1)
+incName (Defined x _) n = Defined x (getNameNum n + 1)
diff --git a/src/Elab/WiredIn.hs b/src/Elab/WiredIn.hs
index 9994428..5a76d90 100644
--- a/src/Elab/WiredIn.hs
+++ b/src/Elab/WiredIn.hs
@@ -22,8 +22,6 @@ import qualified Presyntax.Presyntax as P
 import Syntax
 
 import System.IO.Unsafe
-import GHC.Stack
-import Syntax.Pretty
 
 wiType :: WiredIn -> NFType
 wiType WiType     = VType
@@ -214,7 +212,7 @@ ielim _line _left _right fn i =
         VSystem (Map.toList -> []) -> VSystem (Map.fromList [])
         _ -> error $ "can't ielim " ++ show fn
 
-outS :: HasCallStack => NFSort -> NFEndp -> Value -> Value -> Value
+outS :: NFSort -> NFEndp -> Value -> Value -> Value
 outS _ (force -> VI1) u _  = u @@ VItIsOne
 
 outS _ _phi _ (VInc _ _ x) = x
@@ -245,8 +243,8 @@ comp a psi@phi u (compOutS (a @@ VI1) phi (u @@ VI1 @@ VItIsOne) -> a0) =
                    (VInc (rng VI0 (ybar VI0 arg)) phi (vApp (plic VI0) a0 (ybar VI0 arg)))
     VSigma{} ->
       let
-        dom i = let VSigma d _ = a @@ i in d
-        rng i = let VSigma _ (Closure _ r) = a @@ i in r
+        dom i = let VSigma d _             = force (a @@ i) in d
+        rng i = let VSigma _ (Closure _ r) = force (a @@ i) in r
 
         w i = fill (fun dom) phi (system \i isone -> vProj1 (u @@ i @@ isone)) (VInc (dom VI0) phi (vProj1 a0)) i
         c1 = comp (fun dom) phi (system \i isone -> vProj1 (u @@ i @@ isone)) (VInc (dom VI0) phi (vProj1 a0))
@@ -256,9 +254,9 @@ comp a psi@phi u (compOutS (a @@ VI1) phi (u @@ VI1 @@ VItIsOne) -> a0) =
 
     VPath{} ->
       let
-        a' i = let VPath thea _ _ = a @@ i in thea
-        u' i = let VPath _ theu _ = a @@ i in theu
-        v' i = let VPath _ _ thev = a @@ i in thev
+        a' i = let VPath thea _ _ = force (a @@ i) in thea
+        u' i = let VPath _ theu _ = force (a @@ i) in theu
+        v' i = let VPath _ _ thev = force (a @@ i) in thev
       in
         VLine (a' VI1 @@ VI1) (u' VI1) (v' VI1) $ fun \j ->
           comp (fun a')
@@ -306,7 +304,9 @@ comp a psi@phi u (compOutS (a @@ VI1) phi (u @@ VI1 @@ VItIsOne) -> a0) =
           a1'
         b1 = glueElem (base VI1) (phi VI1) (types VI1) (equivs VI1) (fun (const t1)) a1
        in b1
-    
+
+    VType -> VGlueTy a0 phi (system \_ _ -> u @@ VI1 @@ VItIsOne) (system \_ _  -> makeEquiv (\j -> (u @@ inot j)))
+
     -- fibrancy structure of the booleans is trivial
     VBool{} -> a0
 
@@ -394,14 +394,22 @@ contr a aC phi u =
     (system \i is1 -> ielim (line (const a)) a (vProj1 (u is1)) (vProj2 (u is1)) i)
     (vProj1 aC)
 
+makeEquiv :: (NFEndp -> Value) -> Value
+makeEquiv line = comp (fun \i -> equiv a (line i)) VI0 (system \_ _ -> VSystem mempty) (VPair idfun idisequiv) where
+  a = line VI0
+  idfun = fun id
+-- idEquiv y = ((y, \i -> y), \u i -> (u.2 (inot i), \j -> u.2 (ior (inot i) j)))
+  u_ty = exists' "y" a \x -> VPath (fun (const a)) x x
+  idisequiv = fun \y -> VPair (id_fiber y) $ fun \u ->
+    VLine u_ty (id_fiber y) u $ fun \i -> VPair (ielim (fun (const a)) y y (vProj2 u) i) $
+      VLine (fun (const a)) y (vProj1 u) $ fun \j ->
+        ielim (fun (const a)) y y (vProj2 u) (iand i j)
+
+  id_fiber y = VPair y (VLine a y y (fun (const y)))
+
 elimBool :: NFSort -> Value -> Value -> Value -> Value
 elimBool prop x y bool =
   case force bool of
     VTt -> x
     VFf -> y
-    VNe _ (_ Seq.:|> PIElim _ a b c) ->
-      case c of
-        VI0 -> elimBool prop x y a
-        VI1 -> elimBool prop x y b
-        _ -> VIf prop x y bool
     _ -> VIf prop x y bool
\ No newline at end of file
diff --git a/src/Elab/WiredIn.hs-boot b/src/Elab/WiredIn.hs-boot
index d01be31..9193c1b 100644
--- a/src/Elab/WiredIn.hs-boot
+++ b/src/Elab/WiredIn.hs-boot
@@ -1,7 +1,6 @@
 module Elab.WiredIn where
 
 import Syntax
-import GHC.Stack
 
 wiType  :: WiredIn -> NFType
 wiValue :: WiredIn -> NFType
@@ -10,7 +9,7 @@ iand, ior :: NFEndp -> NFEndp -> NFEndp
 inot      :: NFEndp -> NFEndp
 ielim     :: NFSort -> Value -> Value -> Value -> NFEndp -> Value
 
-outS :: HasCallStack => NFSort -> NFEndp -> Value -> Value -> Value
+outS :: NFSort -> NFEndp -> Value -> Value -> Value
 comp :: NFLine -> NFEndp -> Value -> Value -> Value
 
 glueType :: NFSort -> NFEndp -> NFPartial -> NFPartial -> Value
diff --git a/src/Main.hs b/src/Main.hs
index 7a97b9b..3f97c60 100644
--- a/src/Main.hs
+++ b/src/Main.hs
@@ -8,7 +8,6 @@ module Main where
 import Control.Monad.IO.Class
 import Control.Monad.Reader
 import Control.Exception
-import Control.Monad
 
 import qualified Data.ByteString.Lazy as Bsl
 import qualified Data.Text.Encoding as T