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+module Core.Reduction
+
+import Core.Context
+import Core.Declarative
+import Core.Term
+import Core.Term.Environment
+import Core.Term.Substitution
+
+public export
+data TermStep : Env sx -> Term sx -> Term sx -> Term sx -> Type where
+  PiBeta :
+    TypeWf env f ->
+    TermWf (env :< f) t g ->
+    TermWf env u f ->
+    ---
+    TermStep env (App (Abs n t) u) (subst t $ sub1 u) (subst g $ sub1 u)
+  AppStep :
+    TermStep env t u (Pi n f g) ->
+    TermWf env a f ->
+    ---
+    TermStep env (App t a) (App u a) (subst g $ sub1 a)
+  StepConv :
+    TermStep env t u a ->
+    TypeConv env a b ->
+    ---
+    TermStep env t u b
+
+public export
+TypeStep : Env sx -> Term sx -> Term sx -> Type
+TypeStep env a b = TermStep env a b Set
+
+namespace Type
+  public export
+  data TypeRed : Env sx -> Term sx -> Term sx -> Type where
+    Stay : TypeWf env a -> TypeRed env a a
+    (::) : TypeStep env a b -> TypeRed env b c -> TypeRed env a c
+
+namespace Term
+  public export
+  data TermRed : Env sx -> Term sx -> Term sx -> Term sx -> Type where
+    Stay : TermWf env t a -> TermRed env t t a
+    (::) : TermStep env t u a -> TermRed env u v a -> TermRed env t v a
+
+%name TypeStep step
+%name TermStep step
+%name TypeRed steps
+%name TermRed steps