diff --git a/lib/Quox/Equal.idr b/lib/Quox/Equal.idr
index ea88c5c..c4bcac4 100644
--- a/lib/Quox/Equal.idr
+++ b/lib/Quox/Equal.idr
@@ -285,8 +285,7 @@ parameters (defs : Definitions' q _) {auto _ : (CanEqual q m, Eq q)}
       compare0' _   e@(_ :# _) f        _ _ = clashE e f
 
 
-parameters {auto _ : (HasDefs' q _ m, HasErr q m, Eq q)}
-           (eq : DimEq d) (ctx : TContext q d n)
+parameters {auto _ : (HasDefs' q _ m, HasErr q m, Eq q)} (ctx : TyContext q d n)
   parameters (mode : EqMode)
     namespace Term
       export covering
@@ -294,16 +293,17 @@ parameters {auto _ : (HasDefs' q _ m, HasErr q m, Eq q)}
       compare ty s t = do
         defs <- ask
         runReaderT {m} (MakeEnv {mode}) $
-          for_ (splits eq) $ \th =>
-            compare0 defs (map (/// th) ctx) (ty /// th) (s /// th) (t /// th)
+          for_ (splits ctx.dctx) $ \th =>
+            compare0 defs (map (/// th) ctx.tctx)
+                     (ty /// th) (s /// th) (t /// th)
 
       export covering
       compareType : (s, t : Term q d n) -> m ()
       compareType s t = do
         defs <- ask
         runReaderT {m} (MakeEnv {mode}) $
-          for_ (splits eq) $ \th =>
-            compareType defs (map (/// th) ctx) (s /// th) (t /// th)
+          for_ (splits ctx.dctx) $ \th =>
+            compareType defs (map (/// th) ctx.tctx) (s /// th) (t /// th)
 
     namespace Elim
       ||| you don't have to pass the type in but the arguments must still be
@@ -313,8 +313,8 @@ parameters {auto _ : (HasDefs' q _ m, HasErr q m, Eq q)}
       compare e f = do
         defs <- ask
         runReaderT {m} (MakeEnv {mode}) $
-          for_ (splits eq) $ \th =>
-            compare0 defs (map (/// th) ctx) (e /// th) (f /// th)
+          for_ (splits ctx.dctx) $ \th =>
+            compare0 defs (map (/// th) ctx.tctx) (e /// th) (f /// th)
 
   namespace Term
     export covering %inline
diff --git a/lib/Quox/Typechecker.idr b/lib/Quox/Typechecker.idr
index 02ce914..067efd8 100644
--- a/lib/Quox/Typechecker.idr
+++ b/lib/Quox/Typechecker.idr
@@ -168,9 +168,9 @@ parameters {auto _ : IsQty q} {auto _ : CanTC q m}
     -- if Ψ, i | Γ ⊢ σ · t ⇐ A ⊳ Σ
     qout <- check (extendDim ctx) sg body.term ty.term
     -- if Ψ | Γ ⊢ t‹0› = l : A‹0›
-    equal ctx.dctx ctx.tctx ty.zero body.zero l
+    equal ctx ty.zero body.zero l
     -- if Ψ | Γ ⊢ t‹1› = r : A‹1›
-    equal ctx.dctx ctx.tctx ty.one body.one  r
+    equal ctx ty.one body.one  r
     -- then Ψ | Γ ⊢ σ · (λᴰi ⇒ t) ⇐ Eq [i ⇒ A] l r ⊳ Σ
     pure qout
 
@@ -178,7 +178,7 @@ parameters {auto _ : IsQty q} {auto _ : CanTC q m}
     -- if Ψ | Γ ⊢ σ · e ⇒ A' ⊳ Σ
     infres <- infer ctx sg e
     -- if Ψ | Γ ⊢ A' <: A
-    subtype ctx.dctx ctx.tctx infres.type ty
+    subtype ctx infres.type ty
     -- then Ψ | Γ ⊢ σ · e ⇐ A ⊳ Σ
     pure infres.qout
 
diff --git a/lib/Quox/Typing.idr b/lib/Quox/Typing.idr
index 428f29a..af3afb9 100644
--- a/lib/Quox/Typing.idr
+++ b/lib/Quox/Typing.idr
@@ -44,6 +44,10 @@ namespace TContext
   pushD tel = map (/// shift 1) tel
 
 namespace TyContext
+  public export %inline
+  empty : {d : Nat} -> TyContext q d 0
+  empty = MkTyContext {dctx = new, tctx = [<]}
+
   export %inline
   extendTyN : Telescope (Term q d) from to ->
               TyContext q d from -> TyContext q d to
diff --git a/tests/Tests/Equal.idr b/tests/Tests/Equal.idr
index 5d6789d..73f9b38 100644
--- a/tests/Tests/Equal.idr
+++ b/tests/Tests/Equal.idr
@@ -28,20 +28,24 @@ parameters (label : String) (act : Lazy (M ()))
   testNeq = testThrows label (const True) $ runReaderT globals act
 
 
-parameters {default 0   d, n : Nat}
-           {default new eqs  : DimEq d}
-           (ctx : TContext Three d n)
-  subT : Term Three d n -> Term Three d n -> Term Three d n -> M ()
-  subT ty s t = Term.sub eqs ctx ty s t
+parameters (0 d : Nat) (ctx : TyContext Three d n)
+  subTD, equalTD : Term Three d n -> Term Three d n -> Term Three d n -> M ()
+  subTD ty s t = Term.sub ctx ty s t
+  equalTD ty s t = Term.equal ctx ty s t
 
-  equalT : Term Three d n -> Term Three d n -> Term Three d n -> M ()
-  equalT ty s t = Term.equal eqs ctx ty s t
+  subED, equalED : Elim Three d n -> Elim Three d n -> M ()
+  subED e f = Elim.sub ctx e f
+  equalED e f = Elim.equal ctx e f
 
-  subE : Elim Three d n -> Elim Three d n -> M ()
-  subE e f = Elim.sub eqs ctx e f
+parameters (ctx : TyContext Three 0 n)
+  subT, equalT : Term Three 0 n -> Term Three 0 n -> Term Three 0 n -> M ()
+  subT = subTD 0 ctx
+  equalT = equalTD 0 ctx
+
+  subE, equalE : Elim Three 0 n -> Elim Three 0 n -> M ()
+  subE = subED 0 ctx
+  equalE = equalED 0 ctx
 
-  equalE : Elim Three d n -> Elim Three d n -> M ()
-  equalE e f = Elim.equal eqs ctx e f
 
 
 export
@@ -52,17 +56,17 @@ tests = "equality & subtyping" :- [
 
   "universes" :- [
     testEq "★₀ = ★₀" $
-      equalT [<] (TYPE 1) (TYPE 0) (TYPE 0),
+      equalT empty (TYPE 1) (TYPE 0) (TYPE 0),
     testNeq "★₀ ≠ ★₁" $
-      equalT [<] (TYPE 2) (TYPE 0) (TYPE 1),
+      equalT empty (TYPE 2) (TYPE 0) (TYPE 1),
     testNeq "★₁ ≠ ★₀" $
-      equalT [<] (TYPE 2) (TYPE 1) (TYPE 0),
+      equalT empty (TYPE 2) (TYPE 1) (TYPE 0),
     testEq "★₀ <: ★₀" $
-      subT [<] (TYPE 1) (TYPE 0) (TYPE 0),
+      subT empty (TYPE 1) (TYPE 0) (TYPE 0),
     testEq "★₀ <: ★₁" $
-      subT [<] (TYPE 2) (TYPE 0) (TYPE 1),
+      subT empty (TYPE 2) (TYPE 0) (TYPE 1),
     testNeq "★₁ ≮: ★₀" $
-      subT [<] (TYPE 2) (TYPE 1) (TYPE 0)
+      subT empty (TYPE 2) (TYPE 1) (TYPE 0)
   ],
 
   "pi" :- [
@@ -70,79 +74,79 @@ tests = "equality & subtyping" :- [
     note #""𝐴 ⇾ 𝐵" for (0·𝐴) → 𝐵"#,
     testEq "★₀ ⇾ ★₀ = ★₀ ⇾ ★₀" $
       let tm = Arr Zero (TYPE 0) (TYPE 0) in
-      equalT [<] (TYPE 1) tm tm,
+      equalT empty (TYPE 1) tm tm,
     testEq "★₀ ⇾ ★₀ <: ★₀ ⇾ ★₀" $
       let tm = Arr Zero (TYPE 0) (TYPE 0) in
-      subT [<] (TYPE 1) tm tm,
+      subT empty (TYPE 1) tm tm,
     testNeq "★₁ ⊸ ★₀ ≠ ★₀ ⇾ ★₀" $
       let tm1 = Arr Zero (TYPE 1) (TYPE 0)
           tm2 = Arr Zero (TYPE 0) (TYPE 0) in
-      equalT [<] (TYPE 2) tm1 tm2,
+      equalT empty (TYPE 2) tm1 tm2,
     testEq "★₁ ⊸ ★₀ <: ★₀ ⊸ ★₀" $
       let tm1 = Arr One (TYPE 1) (TYPE 0)
           tm2 = Arr One (TYPE 0) (TYPE 0) in
-      subT [<] (TYPE 2) tm1 tm2,
+      subT empty (TYPE 2) tm1 tm2,
     testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
       let tm1 = Arr One (TYPE 0) (TYPE 0)
           tm2 = Arr One (TYPE 0) (TYPE 1) in
-      subT [<] (TYPE 2) tm1 tm2,
+      subT empty (TYPE 2) tm1 tm2,
     testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
       let tm1 = Arr One (TYPE 0) (TYPE 0)
           tm2 = Arr One (TYPE 0) (TYPE 1) in
-      subT [<] (TYPE 2) tm1 tm2,
+      subT empty (TYPE 2) tm1 tm2,
     testEq "A ⊸ B = A ⊸ B" $
       let tm = Arr One (FT "A") (FT "B") in
-      equalT [<] (TYPE 0) tm tm,
+      equalT empty (TYPE 0) tm tm,
     testEq "A ⊸ B <: A ⊸ B" $
       let tm = Arr One (FT "A") (FT "B") in
-      subT [<] (TYPE 0) tm tm,
+      subT empty (TYPE 0) tm tm,
     note "incompatible quantities",
     testNeq "★₀ ⊸ ★₀ ≠ ★₀ ⇾ ★₁" $
       let tm1 = Arr Zero (TYPE 0) (TYPE 0)
           tm2 = Arr Zero (TYPE 0) (TYPE 1) in
-      equalT [<] (TYPE 2) tm1 tm2,
+      equalT empty (TYPE 2) tm1 tm2,
     testNeq "A ⇾ B ≠ A ⊸ B" $
       let tm1 = Arr Zero (FT "A") (FT "B")
           tm2 = Arr One  (FT "A") (FT "B") in
-      equalT [<] (TYPE 0) tm1 tm2,
+      equalT empty (TYPE 0) tm1 tm2,
     testNeq "A ⇾ B ≮: A ⊸ B" $
       let tm1 = Arr Zero (FT "A") (FT "B")
           tm2 = Arr One  (FT "A") (FT "B") in
-      subT [<] (TYPE 0) tm1 tm2,
+      subT empty (TYPE 0) tm1 tm2,
     testEq "0=1 ⊢ A ⇾ B = A ⊸ B" $
       let tm1 = Arr Zero (FT "A") (FT "B")
           tm2 = Arr One  (FT "A") (FT "B") in
-      equalT [<] (TYPE 0) tm1 tm2 {eqs = ZeroIsOne},
+      equalT (MkTyContext ZeroIsOne [<]) (TYPE 0) tm1 tm2,
     note "[todo] should π ≤ ρ ⊢ (ρ·A) → B <: (π·A) → B?"
   ],
 
   "lambda" :- [
     testEq "λ x ⇒ [x] = λ x ⇒ [x]" $
-      equalT [<] (Arr One (FT "A") (FT "A"))
+      equalT empty (Arr One (FT "A") (FT "A"))
         (["x"] :\\ BVT 0)
         (["x"] :\\ BVT 0),
     testEq "λ x ⇒ [x] <: λ x ⇒ [x]" $
-      subT [<] (Arr One (FT "A") (FT "A"))
+      subT empty (Arr One (FT "A") (FT "A"))
         (["x"] :\\ BVT 0)
         (["x"] :\\ BVT 0),
     testEq "λ x ⇒ [x] = λ y ⇒ [y]" $
-      equalT [<] (Arr One (FT "A") (FT "A"))
+      equalT empty (Arr One (FT "A") (FT "A"))
         (["x"] :\\ BVT 0)
         (["y"] :\\ BVT 0),
     testEq "λ x ⇒ [x] <: λ y ⇒ [y]" $
-      equalT [<] (Arr One (FT "A") (FT "A"))
+      equalT empty (Arr One (FT "A") (FT "A"))
         (["x"] :\\ BVT 0)
         (["y"] :\\ BVT 0),
     testNeq "λ x y ⇒ [x] ≠ λ x y ⇒ [y]" $
-      equalT [<] (Arr One (FT "A") $ Arr One (FT "A") (FT "A"))
+      equalT empty (Arr One (FT "A") $ Arr One (FT "A") (FT "A"))
         (["x", "y"] :\\ BVT 1)
         (["x", "y"] :\\ BVT 0),
     testEq "λ x ⇒ [a] = λ x ⇒ [a]  (TUsed vs TUnused)" $
-      equalT [<] (Arr Zero (FT "B") (FT "A"))
+      equalT empty (Arr Zero (FT "B") (FT "A"))
         (Lam "x" $ TUsed   $ FT "a")
         (Lam "x" $ TUnused $ FT "a"),
     testEq "λ x ⇒ [f [x]] = [f]  (η)" $
-      equalT [<] (Arr One (FT "A") (FT "A"))
+      equalT empty (Arr One (FT "A") (FT "A"))
         (["x"] :\\ E (F "f" :@ BVT 0))
         (FT "f")
   ],
@@ -150,10 +154,10 @@ tests = "equality & subtyping" :- [
   "eq type" :- [
     testEq "(★₀ ≡ ★₀ : ★₁) = (★₀ ≡ ★₀ : ★₁)" $
       let tm = Eq0 (TYPE 1) (TYPE 0) (TYPE 0) in
-      equalT [<] (TYPE 2) tm tm,
+      equalT empty (TYPE 2) tm tm,
     testEq "A ≔ ★₁ ⊢ (★₀ ≡ ★₀ : ★₁) = (★₀ ≡ ★₀ : A)"
         {globals = fromList [("A", mkDef zero (TYPE 2) (TYPE 1))]} $
-      equalT [<] (TYPE 2)
+      equalT empty (TYPE 2)
         (Eq0 (TYPE 1) (TYPE 0) (TYPE 0))
         (Eq0 (FT "A") (TYPE 0) (TYPE 0))
   ],
@@ -166,86 +170,86 @@ tests = "equality & subtyping" :- [
     note #""refl [A] x" is an abbreviation for "(λᴰi ⇒ x) ∷ (x ≡ x : A)""#,
     note "binds before ∥ are globals, after it are BVs",
     testEq "refl [A] a = refl [A] a" $
-      equalE [<] (refl (FT "A") (FT "a")) (refl (FT "A") (FT "a")),
+      equalE empty (refl (FT "A") (FT "a")) (refl (FT "A") (FT "a")),
 
     testEq "p : (a ≡ a' : A), q : (a ≡ a' : A) ∥ ⊢ p = q  (free)"
            {globals =
               let def = mkAbstract Zero $ Eq0 (FT "A") (FT "a") (FT "a'") in
               defGlobals `mergeLeft` fromList [("p", def), ("q", def)]} $
-      equalE [<] (F "p") (F "q"),
+      equalE empty (F "p") (F "q"),
 
     testEq "∥ x : (a ≡ a' : A), y : (a ≡ a' : A) ⊢ x = y  (bound)" $
       let ty : forall n. Term Three 0 n := Eq0 (FT "A") (FT "a") (FT "a'") in
-      equalE [< ty, ty] (BV 0) (BV 1) {n = 2},
+      equalE (MkTyContext new [< ty, ty]) (BV 0) (BV 1),
 
     testEq "∥ x : [(a ≡ a' : A) ∷ Type 0], y : [ditto] ⊢ x = y" $
       let ty :  forall n. Term Three 0 n
              := E (Eq0 (FT "A") (FT "a") (FT "a'") :# TYPE 0) in
-      equalE [< ty, ty] (BV 0) (BV 1) {n = 2},
+      equalE (MkTyContext new [< ty, ty]) (BV 0) (BV 1),
 
     testEq "E ≔ a ≡ a' : A, EE ≔ E ∥ x : EE, y : EE ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
               [("E", mkDef zero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'"))),
                ("EE", mkDef zero (TYPE 0) (FT "E"))]} $
-      equalE [< FT "EE", FT "EE"] (BV 0) (BV 1) {n = 2},
+      equalE (MkTyContext new [< FT "EE", FT "EE"]) (BV 0) (BV 1),
 
     testEq "E ≔ a ≡ a' : A, EE ≔ E ∥ x : EE, y : E ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
               [("E", mkDef zero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'"))),
                ("EE", mkDef zero (TYPE 0) (FT "E"))]} $
-      equalE [< FT "EE", FT "E"] (BV 0) (BV 1) {n = 2},
+      equalE (MkTyContext new [< FT "EE", FT "E"]) (BV 0) (BV 1),
 
     testEq "E ≔ a ≡ a' : A ∥ x : E, y : E ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
               [("E", mkDef zero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'")))]} $
-      equalE [< FT "E", FT "E"] (BV 0) (BV 1) {n = 2},
+      equalE (MkTyContext new [< FT "E", FT "E"]) (BV 0) (BV 1),
 
     testEq "E ≔ a ≡ a' : A ∥ x : (E×E), y : (E×E) ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
               [("E", mkDef zero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'")))]} $
       let ty :  forall n. Term Three 0 n
              := Sig "_" (FT "E") $ TUnused $ FT "E" in
-      equalE [< ty, ty] (BV 0) (BV 1) {n = 2},
+      equalE (MkTyContext new [< ty, ty]) (BV 0) (BV 1),
 
     testEq "E ≔ a ≡ a' : A, F ≔ E × E ∥ x : F, y : F ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
               [("E", mkDef zero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'"))),
                ("W", mkDef zero (TYPE 0) (FT "E" `And` FT "E"))]} $
-      equalE [< FT "W", FT "W"] (BV 0) (BV 1) {n = 2}
+      equalE (MkTyContext new [< FT "W", FT "W"]) (BV 0) (BV 1)
   ],
 
   "term closure" :- [
     testEq "[#0]{} = [#0] : A" $
-      equalT [< FT "A"] (FT "A") {n = 1}
+      equalT (MkTyContext new [< FT "A"]) (FT "A")
         (CloT (BVT 0) id)
         (BVT 0),
     testEq "[#0]{a} = [a] : A" $
-      equalT [<] (FT "A")
+      equalT empty (FT "A")
         (CloT (BVT 0) (F "a" ::: id))
         (FT "a"),
     testEq "[#0]{a,b} = [a] : A" $
-      equalT [<] (FT "A")
+      equalT empty (FT "A")
         (CloT (BVT 0) (F "a" ::: F "b" ::: id))
         (FT "a"),
     testEq "[#1]{a,b} = [b] : A" $
-      equalT [<] (FT "A")
+      equalT empty (FT "A")
         (CloT (BVT 1) (F "a" ::: F "b" ::: id))
         (FT "b"),
     testEq "(λy. [#1]){a} = λy. [a] : B ⇾ A  (TUnused)" $
-      equalT [<] (Arr Zero (FT "B") (FT "A"))
+      equalT empty (Arr Zero (FT "B") (FT "A"))
         (CloT (Lam "y" $ TUnused $ BVT 0) (F "a" ::: id))
         (Lam "y" $ TUnused $ FT "a"),
     testEq "(λy. [#1]){a} = λy. [a] : B ⇾ A  (TUsed)" $
-      equalT [<] (Arr Zero (FT "B") (FT "A"))
+      equalT empty (Arr Zero (FT "B") (FT "A"))
         (CloT (["y"] :\\ BVT 1) (F "a" ::: id))
         (["y"] :\\ FT "a")
   ],
 
   "term d-closure" :- [
     testEq "★₀‹𝟎› = ★₀ : ★₁" $
-      equalT {d = 1} [<] (TYPE 1) (DCloT (TYPE 0) (K Zero ::: id)) (TYPE 0),
+      equalTD 1 empty (TYPE 1) (DCloT (TYPE 0) (K Zero ::: id)) (TYPE 0),
     testEq "(λᴰ i ⇒ a)‹𝟎› = (λᴰ i ⇒ a) : (a ≡ a : A)" $
-      equalT {d = 1} [<]
+      equalTD 1 empty
         (Eq0 (FT "A") (FT "a") (FT "a"))
         (DCloT (["i"] :\\% FT "a") (K Zero ::: id))
         (["i"] :\\% FT "a"),
@@ -261,136 +265,137 @@ tests = "equality & subtyping" :- [
          ("B", mkDef Any (TYPE (U 1)) (FT "A"))]
   in [
     testEq "A = A" $
-      equalE [<] (F "A") (F "A"),
+      equalE empty (F "A") (F "A"),
     testNeq "A ≠ B" $
-      equalE [<] (F "A") (F "B"),
+      equalE empty (F "A") (F "B"),
     testEq "0=1 ⊢ A = B" $
-      equalE {eqs = ZeroIsOne} [<] (F "A") (F "B"),
+      equalE (MkTyContext ZeroIsOne [<]) (F "A") (F "B"),
     testEq "A : ★₁ ≔ ★₀ ⊢ A = (★₀ ∷ ★₁)" {globals = au_bu} $
-      equalE [<] (F "A") (TYPE 0 :# TYPE 1),
+      equalE empty (F "A") (TYPE 0 :# TYPE 1),
     testEq "A : ★₁ ≔ ★₀ ⊢ [A] = ★₀" {globals = au_bu} $
-      equalT [<] (TYPE 1) (FT "A") (TYPE 0),
+      equalT empty (TYPE 1) (FT "A") (TYPE 0),
     testEq "A ≔ ★₀, B ≔ ★₀ ⊢ A = B" {globals = au_bu} $
-      equalE [<] (F "A") (F "B"),
+      equalE empty (F "A") (F "B"),
     testEq "A ≔ ★₀, B ≔ A ⊢ A = B" {globals = au_ba} $
-      equalE [<] (F "A") (F "B"),
+      equalE empty (F "A") (F "B"),
     testEq "A <: A" $
-      subE [<] (F "A") (F "A"),
+      subE empty (F "A") (F "A"),
     testNeq "A ≮: B" $
-      subE [<] (F "A") (F "B"),
+      subE empty (F "A") (F "B"),
     testEq "A : ★₃ ≔ ★₀, B : ★₃ ≔ ★₂ ⊢ A <: B"
         {globals = fromList [("A", mkDef Any (TYPE 3) (TYPE 0)),
                              ("B", mkDef Any (TYPE 3) (TYPE 2))]} $
-      subE [<] (F "A") (F "B"),
+      subE empty (F "A") (F "B"),
     note "(A and B in different universes)",
     testEq "A : ★₁ ≔ ★₀, B : ★₃ ≔ ★₂ ⊢ A <: B"
         {globals = fromList [("A", mkDef Any (TYPE 1) (TYPE 0)),
                              ("B", mkDef Any (TYPE 3) (TYPE 2))]} $
-      subE [<] (F "A") (F "B"),
+      subE empty (F "A") (F "B"),
     testEq "0=1 ⊢ A <: B" $
-      subE [<] (F "A") (F "B") {eqs = ZeroIsOne}
+      subE (MkTyContext ZeroIsOne [<]) (F "A") (F "B")
   ],
 
   "bound var" :- [
     testEq "#0 = #0" $
-      equalE [< TYPE 0] (BV 0) (BV 0) {n = 1},
+      equalE (MkTyContext new [< TYPE 0]) (BV 0) (BV 0),
     testEq "#0 <: #0" $
-      subE [< TYPE 0] (BV 0) (BV 0) {n = 1},
+      subE (MkTyContext new [< TYPE 0]) (BV 0) (BV 0),
     testNeq "#0 ≠ #1" $
-      equalE [< TYPE 0, TYPE 0] (BV 0) (BV 1) {n = 2},
+      equalE (MkTyContext new [< TYPE 0, TYPE 0]) (BV 0) (BV 1),
     testNeq "#0 ≮: #1" $
-      subE [< TYPE 0, TYPE 0] (BV 0) (BV 1) {n = 2},
+      subE (MkTyContext new [< TYPE 0, TYPE 0]) (BV 0) (BV 1),
     testEq "0=1 ⊢ #0 = #1" $
-      equalE [< TYPE 0, TYPE 0] (BV 0) (BV 1)
-        {n = 2, eqs = ZeroIsOne}
+      equalE (MkTyContext ZeroIsOne [< TYPE 0, TYPE 0]) (BV 0) (BV 1)
   ],
 
   "application" :- [
     testEq "f [a] = f [a]" $
-      equalE [<] (F "f" :@ FT "a") (F "f" :@ FT "a"),
+      equalE empty (F "f" :@ FT "a") (F "f" :@ FT "a"),
     testEq "f [a] <: f [a]" $
-      subE [<] (F "f" :@ FT "a") (F "f" :@ FT "a"),
+      subE empty (F "f" :@ FT "a") (F "f" :@ FT "a"),
     testEq "(λ x ⇒ [x] ∷ A ⊸ A) a = ([a ∷ A] ∷ A)  (β)" $
-      equalE [<]
+      equalE empty
         (((["x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
         (E (FT "a" :# FT "A") :# FT "A"),
     testEq "(λ x ⇒ [x] ∷ A ⊸ A) a = a  (βυ)" $
-      equalE [<]
+      equalE empty
         (((["x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
         (F "a"),
     testEq "(λ g ⇒ [g [a]] ∷ ⋯)) [f] = (λ y ⇒ [f [y]] ∷ ⋯) [a]  (β↘↙)" $
       let a = FT "A"; a2a = (Arr One a a) in
-      equalE [<]
+      equalE empty
         (((["g"] :\\ E (BV 0 :@ FT "a")) :# Arr One a2a a) :@ FT "f")
         (((["y"] :\\ E (F "f" :@ BVT 0)) :# a2a) :@ FT "a"),
     testEq "(λ x ⇒ [x] ∷ A ⊸ A) a <: a" $
-      subE [<]
+      subE empty
         (((["x"] :\\ BVT 0) :# (Arr One (FT "A") (FT "A"))) :@ FT "a")
         (F "a"),
     note "id : A ⊸ A ≔ λ x ⇒ [x]",
-    testEq "id [a] = a" $ equalE [<] (F "id" :@ FT "a") (F "a"),
-    testEq "id [a] <: a" $ subE [<] (F "id" :@ FT "a") (F "a")
+    testEq "id [a] = a" $ equalE empty (F "id" :@ FT "a") (F "a"),
+    testEq "id [a] <: a" $ subE empty (F "id" :@ FT "a") (F "a")
   ],
 
   todo "dim application",
 
   "annotation" :- [
     testEq "(λ x ⇒ f [x]) ∷ A ⊸ A = [f] ∷ A ⊸ A" $
-      equalE [<]
+      equalE empty
         ((["x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
         (FT "f" :# Arr One (FT "A") (FT "A")),
     testEq "[f] ∷ A ⊸ A = f" $
-      equalE [<] (FT "f" :# Arr One (FT "A") (FT "A")) (F "f"),
+      equalE empty (FT "f" :# Arr One (FT "A") (FT "A")) (F "f"),
     testEq "(λ x ⇒ f [x]) ∷ A ⊸ A = f" $
-      equalE [<]
+      equalE empty
         ((["x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
         (F "f")
   ],
 
   "elim closure" :- [
     testEq "#0{a} = a" $
-      equalE [<] (CloE (BV 0) (F "a" ::: id)) (F "a"),
+      equalE empty (CloE (BV 0) (F "a" ::: id)) (F "a"),
     testEq "#1{a} = #0" $
-      equalE [< FT "A"] (CloE (BV 1) (F "a" ::: id)) (BV 0) {n = 1}
+      equalE (MkTyContext new [< FT "A"])
+        (CloE (BV 1) (F "a" ::: id)) (BV 0)
   ],
 
   "elim d-closure" :- [
     note "0·eq-ab : (A ≡ B : ★₀)",
     testEq "(eq-ab #0)‹𝟎› = eq-ab 𝟎" $
-      equalE {d = 1} [<]
+      equalED 1 empty
         (DCloE (F "eq-ab" :% BV 0) (K Zero ::: id))
         (F "eq-ab" :% K Zero),
     testEq "(eq-ab #0)‹𝟎› = A" $
-      equalE {d = 1} [<] (DCloE (F "eq-ab" :% BV 0) (K Zero ::: id)) (F "A"),
+      equalED 1 empty (DCloE (F "eq-ab" :% BV 0) (K Zero ::: id)) (F "A"),
     testEq "(eq-ab #0)‹𝟏› = B" $
-      equalE {d = 1} [<] (DCloE (F "eq-ab" :% BV 0) (K One  ::: id)) (F "B"),
+      equalED 1 empty (DCloE (F "eq-ab" :% BV 0) (K One  ::: id)) (F "B"),
     testNeq "(eq-ab #0)‹𝟏› ≠ A" $
-      equalE {d = 1} [<] (DCloE (F "eq-ab" :% BV 0) (K One  ::: id)) (F "A"),
+      equalED 1 empty (DCloE (F "eq-ab" :% BV 0) (K One  ::: id)) (F "A"),
     testEq "(eq-ab #0)‹#0,𝟎› = (eq-ab #0)" $
-      equalE {d = 2} [<]
+      equalED 2 empty
         (DCloE (F "eq-ab" :% BV 0) (BV 0 ::: K Zero ::: id))
         (F "eq-ab" :% BV 0),
     testNeq "(eq-ab #0)‹𝟎› ≠ (eq-ab 𝟎)" $
-      equalE {d = 2} [<]
+      equalED 2 empty
         (DCloE (F "eq-ab" :% BV 0) (BV 0 ::: K Zero ::: id))
         (F "eq-ab" :% K Zero),
     testEq "#0‹𝟎› = #0  # term and dim vars distinct" $
-      equalE {d = 1, n = 1} [< FT "A"] (DCloE (BV 0) (K Zero ::: id)) (BV 0),
+      equalED 1 (MkTyContext new [< FT "A"])
+        (DCloE (BV 0) (K Zero ::: id)) (BV 0),
     testEq "a‹𝟎› = a" $
-      equalE {d = 1} [<] (DCloE (F "a") (K Zero ::: id)) (F "a"),
+      equalED 1 empty (DCloE (F "a") (K Zero ::: id)) (F "a"),
     testEq "(f [a])‹𝟎› = f‹𝟎› [a]‹𝟎›" $
       let th = (K Zero ::: id) in
-      equalE {d = 1} [<]
+      equalED 1 empty
         (DCloE (F "f" :@ FT "a") th)
         (DCloE (F "f") th :@ DCloT (FT "a") th)
   ],
 
   "clashes" :- [
     testNeq "★₀ ≠ ★₀ ⇾ ★₀" $
-      equalT [<] (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
+      equalT empty (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
     testEq "0=1 ⊢ ★₀ = ★₀ ⇾ ★₀" $
-      equalT [<] (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0))
-        {eqs = ZeroIsOne},
+      equalT (MkTyContext ZeroIsOne [<])
+        (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
     todo "others"
   ]
 ]
diff --git a/tests/Tests/Typechecker.idr b/tests/Tests/Typechecker.idr
index 2126bf3..6d8f931 100644
--- a/tests/Tests/Typechecker.idr
+++ b/tests/Tests/Typechecker.idr
@@ -75,7 +75,7 @@ ctx = MkTyContext new
 inferredTypeEq : TyContext Three d n -> (exp, got : Term Three d n) -> M ()
 inferredTypeEq ctx exp got =
   catchError
-    (inj $ equalType ctx.dctx ctx.tctx exp got)
+    (inj $ equalType ctx exp got)
     (\_ : Error' => throwError $ WrongInfer exp got)
 
 qoutEq : (exp, got : QOutput Three n) -> M ()