Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Inductive eval_builtin_arg: builtin_arg A -> val -> Prop :=
  | eval_BA: forall x,
      eval_builtin_arg (BA x) (e x)
  | eval_BA_int: forall n,
      eval_builtin_arg (BA_int n) (Vint n)
  | eval_BA_long: forall n,
      eval_builtin_arg (BA_long n) (Vlong n)
  | eval_BA_float: forall n,
      eval_builtin_arg (BA_float n) (Vfloat n)
  | eval_BA_single: forall n,
      eval_builtin_arg (BA_single n) (Vsingle n)
  | eval_BA_loadstack: forall chunk ofs v,
      Mem.loadv chunk m (Val.offset_ptr sp ofs) = Some v ->
      eval_builtin_arg (BA_loadstack chunk ofs) v
  | eval_BA_addrstack: forall ofs,
      eval_builtin_arg (BA_addrstack ofs) (Val.offset_ptr sp ofs)
  | eval_BA_loadglobal: forall chunk id ofs v,
      Mem.loadv chunk m (Senv.symbol_address ge id ofs) = Some v ->
      eval_builtin_arg (BA_loadglobal chunk id ofs) v
  | eval_BA_addrglobal: forall id ofs,
      eval_builtin_arg (BA_addrglobal id ofs) (Senv.symbol_address ge id ofs)
  | eval_BA_splitlong: forall hi lo vhi vlo,
      eval_builtin_arg hi vhi -> eval_builtin_arg lo vlo ->
      eval_builtin_arg (BA_splitlong hi lo) (Val.longofwords vhi vlo)
  | eval_BA_addptr: forall a1 a2 v1 v2,
      eval_builtin_arg a1 v1 -> eval_builtin_arg a2 v2 ->
      eval_builtin_arg (BA_addptr a1 a2)
                       (if Archi.ptr64 then Val.addl v1 v2 else Val.add v1 v2).Definition eval_builtin_args (al: list (builtin_arg A)) (vl: list val) : Prop :=
  list_forall2 eval_builtin_arg al vl.

(* Specifications: *)
Lemma eval_builtin_arg_determ: forall a v, eval_builtin_arg a v -> forall v', eval_builtin_arg a v' -> v' = v.
Lemma eval_builtin_args_determ: forall al vl, eval_builtin_args al vl -> forall vl', eval_builtin_args al vl' -> vl' = vl.
Lemma eval_builtin_arg_preserved: forall a v, eval_builtin_arg ge1 e sp m a v -> eval_builtin_arg ge2 e sp m a v.
Lemma eval_builtin_args_preserved: forall al vl, eval_builtin_args ge1 e sp m al vl -> eval_builtin_args ge2 e sp m al vl.
Lemma eval_builtin_arg_lessdef: forall a v1, eval_builtin_arg ge e1 sp m1 a v1 -> exists v2, eval_builtin_arg ge e2 sp m2 a v2 /\ Val.lessdef v1 v2.
Lemma eval_builtin_args_lessdef: forall al vl1, eval_builtin_args ge e1 sp m1 al vl1 -> exists vl2, eval_builtin_args ge e2 sp m2 al vl2 /\ Val.lessdef_list vl1 vl2.
Lemma eval_builtin_arg_determ: forall a v, eval_builtin_arg a v -> forall v', eval_builtin_arg a v' -> v' = v.
Lemma eval_builtin_args_determ: forall al vl, eval_builtin_args al vl -> forall vl', eval_builtin_args al vl' -> vl' = vl.
Lemma eval_builtin_arg_preserved: forall a v, eval_builtin_arg ge1 e sp m a v -> eval_builtin_arg ge2 e sp m a v.
Lemma eval_builtin_args_preserved: forall al vl, eval_builtin_args ge1 e sp m al vl -> eval_builtin_args ge2 e sp m al vl.
Lemma eval_builtin_arg_lessdef: forall a v1, eval_builtin_arg ge e1 sp m1 a v1 -> exists v2, eval_builtin_arg ge e2 sp m2 a v2 /\ Val.lessdef v1 v2.
Lemma eval_builtin_args_lessdef: forall al vl1, eval_builtin_args ge e1 sp m1 al vl1 -> exists vl2, eval_builtin_args ge e2 sp m2 al vl2 /\ Val.lessdef_list vl1 vl2.