Inductive val_content_inject (f: meminj): memory_chunk -> val -> val -> Prop :=
  | val_content_inject_8_signed:
      forall n1 n2, Int.sign_ext 8 n1 = Int.sign_ext 8 n2 ->
      val_content_inject f Mint8signed (Vint n1) (Vint n2)
  | val_content_inject_8_unsigned:
      forall n1 n2, Int.zero_ext 8 n1 = Int.zero_ext 8 n2 ->
      val_content_inject f Mint8unsigned (Vint n1) (Vint n2)
  | val_content_inject_16_signed:
      forall n1 n2, Int.sign_ext 16 n1 = Int.sign_ext 16 n2 ->
      val_content_inject f Mint16signed (Vint n1) (Vint n2)
  | val_content_inject_16_unsigned:
      forall n1 n2, Int.zero_ext 16 n1 = Int.zero_ext 16 n2 ->
      val_content_inject f Mint16unsigned (Vint n1) (Vint n2)
  | val_content_inject_single:
      forall n1 n2, Float.singleoffloat n1 = Float.singleoffloat n2 ->
      val_content_inject f Mfloat32 (Vfloat n1) (Vfloat n2)
  | val_content_inject_base:
      forall chunk v1 v2, val_inject f v1 v2 ->
      val_content_inject f chunk v1 v2.Inductive val_content_inject (f: meminj): memory_chunk -> val -> val -> Prop :=
  | val_content_inject_8_signed:
      forall n1 n2, Int.sign_ext 8 n1 = Int.sign_ext 8 n2 ->
      val_content_inject f Mint8signed (Vint n1) (Vint n2)
  | val_content_inject_8_unsigned:
      forall n1 n2, Int.zero_ext 8 n1 = Int.zero_ext 8 n2 ->
      val_content_inject f Mint8unsigned (Vint n1) (Vint n2)
  | val_content_inject_16_signed:
      forall n1 n2, Int.sign_ext 16 n1 = Int.sign_ext 16 n2 ->
      val_content_inject f Mint16signed (Vint n1) (Vint n2)
  | val_content_inject_16_unsigned:
      forall n1 n2, Int.zero_ext 16 n1 = Int.zero_ext 16 n2 ->
      val_content_inject f Mint16unsigned (Vint n1) (Vint n2)
  | val_content_inject_single:
      forall n1 n2, Float.singleoffloat n1 = Float.singleoffloat n2 ->
      val_content_inject f Mfloat32 (Vfloat n1) (Vfloat n2)
  | val_content_inject_base:
      forall chunk v1 v2, val_inject f v1 v2 ->
      val_content_inject f chunk v1 v2.Inductive val_content_inject (f: meminj): memory_chunk -> val -> val -> Prop :=
  | val_content_inject_8_signed:
      forall n1 n2, Int.sign_ext 8 n1 = Int.sign_ext 8 n2 ->
      val_content_inject f Mint8signed (Vint n1) (Vint n2)
  | val_content_inject_8_unsigned:
      forall n1 n2, Int.zero_ext 8 n1 = Int.zero_ext 8 n2 ->
      val_content_inject f Mint8unsigned (Vint n1) (Vint n2)
  | val_content_inject_16_signed:
      forall n1 n2, Int.sign_ext 16 n1 = Int.sign_ext 16 n2 ->
      val_content_inject f Mint16signed (Vint n1) (Vint n2)
  | val_content_inject_16_unsigned:
      forall n1 n2, Int.zero_ext 16 n1 = Int.zero_ext 16 n2 ->
      val_content_inject f Mint16unsigned (Vint n1) (Vint n2)
  | val_content_inject_single:
      forall n1 n2, Float.singleoffloat n1 = Float.singleoffloat n2 ->
      val_content_inject f Mfloat32 (Vfloat n1) (Vfloat n2)
  | val_content_inject_base:
      forall chunk v1 v2, val_inject f v1 v2 ->
      val_content_inject f chunk v1 v2.Inductive val_content_inject (f: meminj): memory_chunk -> val -> val -> Prop :=
  | val_content_inject_8_signed:
      forall n1 n2, Int.sign_ext 8 n1 = Int.sign_ext 8 n2 ->
      val_content_inject f Mint8signed (Vint n1) (Vint n2)
  | val_content_inject_8_unsigned:
      forall n1 n2, Int.zero_ext 8 n1 = Int.zero_ext 8 n2 ->
      val_content_inject f Mint8unsigned (Vint n1) (Vint n2)
  | val_content_inject_16_signed:
      forall n1 n2, Int.sign_ext 16 n1 = Int.sign_ext 16 n2 ->
      val_content_inject f Mint16signed (Vint n1) (Vint n2)
  | val_content_inject_16_unsigned:
      forall n1 n2, Int.zero_ext 16 n1 = Int.zero_ext 16 n2 ->
      val_content_inject f Mint16unsigned (Vint n1) (Vint n2)
  | val_content_inject_single:
      forall n1 n2, Float.singleoffloat n1 = Float.singleoffloat n2 ->
      val_content_inject f Mfloat32 (Vfloat n1) (Vfloat n2)
  | val_content_inject_base:
      forall chunk v1 v2, val_inject f v1 v2 ->
      val_content_inject f chunk v1 v2.Inductive val_content_inject (f: meminj): memory_chunk -> val -> val -> Prop :=
  | val_content_inject_8_signed:
      forall n1 n2, Int.sign_ext 8 n1 = Int.sign_ext 8 n2 ->
      val_content_inject f Mint8signed (Vint n1) (Vint n2)
  | val_content_inject_8_unsigned:
      forall n1 n2, Int.zero_ext 8 n1 = Int.zero_ext 8 n2 ->
      val_content_inject f Mint8unsigned (Vint n1) (Vint n2)
  | val_content_inject_16_signed:
      forall n1 n2, Int.sign_ext 16 n1 = Int.sign_ext 16 n2 ->
      val_content_inject f Mint16signed (Vint n1) (Vint n2)
  | val_content_inject_16_unsigned:
      forall n1 n2, Int.zero_ext 16 n1 = Int.zero_ext 16 n2 ->
      val_content_inject f Mint16unsigned (Vint n1) (Vint n2)
  | val_content_inject_single:
      forall n1 n2, Float.singleoffloat n1 = Float.singleoffloat n2 ->
      val_content_inject f Mfloat32 (Vfloat n1) (Vfloat n2)
  | val_content_inject_base:
      forall chunk v1 v2, val_inject f v1 v2 ->
      val_content_inject f chunk v1 v2.Inductive val_content_inject (f: meminj): memory_chunk -> val -> val -> Prop :=
  | val_content_inject_8_signed:
      forall n1 n2, Int.sign_ext 8 n1 = Int.sign_ext 8 n2 ->
      val_content_inject f Mint8signed (Vint n1) (Vint n2)
  | val_content_inject_8_unsigned:
      forall n1 n2, Int.zero_ext 8 n1 = Int.zero_ext 8 n2 ->
      val_content_inject f Mint8unsigned (Vint n1) (Vint n2)
  | val_content_inject_16_signed:
      forall n1 n2, Int.sign_ext 16 n1 = Int.sign_ext 16 n2 ->
      val_content_inject f Mint16signed (Vint n1) (Vint n2)
  | val_content_inject_16_unsigned:
      forall n1 n2, Int.zero_ext 16 n1 = Int.zero_ext 16 n2 ->
      val_content_inject f Mint16unsigned (Vint n1) (Vint n2)
  | val_content_inject_single:
      forall n1 n2, Float.singleoffloat n1 = Float.singleoffloat n2 ->
      val_content_inject f Mfloat32 (Vfloat n1) (Vfloat n2)
  | val_content_inject_base:
      forall chunk v1 v2, val_inject f v1 v2 ->
      val_content_inject f chunk v1 v2.Inductive val_content_inject (f: meminj): memory_chunk -> val -> val -> Prop :=
  | val_content_inject_8_signed:
      forall n1 n2, Int.sign_ext 8 n1 = Int.sign_ext 8 n2 ->
      val_content_inject f Mint8signed (Vint n1) (Vint n2)
  | val_content_inject_8_unsigned:
      forall n1 n2, Int.zero_ext 8 n1 = Int.zero_ext 8 n2 ->
      val_content_inject f Mint8unsigned (Vint n1) (Vint n2)
  | val_content_inject_16_signed:
      forall n1 n2, Int.sign_ext 16 n1 = Int.sign_ext 16 n2 ->
      val_content_inject f Mint16signed (Vint n1) (Vint n2)
  | val_content_inject_16_unsigned:
      forall n1 n2, Int.zero_ext 16 n1 = Int.zero_ext 16 n2 ->
      val_content_inject f Mint16unsigned (Vint n1) (Vint n2)
  | val_content_inject_single:
      forall n1 n2, Float.singleoffloat n1 = Float.singleoffloat n2 ->
      val_content_inject f Mfloat32 (Vfloat n1) (Vfloat n2)
  | val_content_inject_base:
      forall chunk v1 v2, val_inject f v1 v2 ->
      val_content_inject f chunk v1 v2.

Lemma storev_mapped_content_inject: forall f chunk m1 a1 v1 n1 m2 a2 v2, Mem.inject f m1 m2 -> Mem.storev chunk m1 a1 v1 = Some n1 -> val_inject f a1 a2 -> val_content_inject f chunk v1 v2 -> exists n2, Mem.storev chunk m2 a2 v2 = Some n2 /\ Mem.inject f n1 n2.