define Data.Set.Base.singleton x      = (Set_sng x)
define Data.Set.Base.union x y        = (Set_cup x y)
define Data.Set.Base.intersection x y = (Set_cap x y)
define Data.Set.Base.difference x y   = (Set_dif x y)
define Data.Set.Base.empty            = (Set_empty 0)
define Data.Set.Base.null x           = (Set_emp x)
define Data.Set.Base.member x xs      = (Set_mem x xs)
define Data.Set.Base.isSubsetOf x y   = (Set_sub x y)
define Data.Set.Base.fromList xs      = (listElts xs)

define Data.Set.Internal.singleton x      = (Set_sng x)
define Data.Set.Internal.union x y        = (Set_cup x y)
define Data.Set.Internal.intersection x y = (Set_cap x y)
define Data.Set.Internal.difference x y   = (Set_dif x y)
define Data.Set.Internal.empty            = (Set_empty 0)
define Data.Set.Internal.null x           = (Set_emp x)
define Data.Set.Internal.member x xs      = (Set_mem x xs)
define Data.Set.Internal.isSubsetOf x y   = (Set_sub x y)
define Data.Set.Internal.fromList xs      = (listElts xs)

define GHC.Real.fromIntegral x = (x)

define GHC.Types.True                 = (true)
define GHC.Real.div x y               = (x / y)
define GHC.Real.mod x y               = (x mod y)
define GHC.Base.$ f x                 = (f x)

define Language.Haskell.Liquid.Bag.get k m   = (Map_select m k)
define Language.Haskell.Liquid.Bag.put k m   = (Map_store m k (1 + (Map_select m k)))
define Language.Haskell.Liquid.Bag.union m n = (Map_union  m n)
define Language.Haskell.Liquid.Bag.empty     = (Map_default 0)

define Data.Map.Base.insert k v m     = (Map_store m k v)
define Data.Map.Base.select k v       = (Map_select m k)

define Language.Haskell.Liquid.String.stringEmp = (stringEmp)
define Data.RString.RString.stringEmp = (stringEmp)
define String.stringEmp  = (stringEmp)
define Main.mempty       = (mempty)
define Language.Haskell.Liquid.ProofCombinators.cast x y = (y)
define ProofCombinators.cast x y = (y)
define Control.Parallel.Strategies.withStrategy s x = (x)

define ProofCombinators.cast x y = (y)
define Language.Haskell.Liquid.Equational.eq x y = (y)

define GHC.CString.unpackCString# x = x