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