Definition injective_PTree A := sig (@PTree_injective A).Structure external_specification (M E Z : Type) :=
  { ext_spec_type : E -> Type
  ; ext_spec_pre: forall e: E,
    ext_spec_type e -> injective_PTree block -> list typ -> list val -> Z -> M -> Prop
  ; ext_spec_post: forall e: E,
    ext_spec_type e -> injective_PTree block -> option typ -> option val -> Z -> M ->  Prop
  ; ext_spec_exit: option val -> Z -> M ->  Prop }.Structure external_specification (M E Z : Type) :=
  { ext_spec_type : E -> Type
  ; ext_spec_pre: forall e: E,
    ext_spec_type e -> injective_PTree block -> list typ -> list val -> Z -> M -> Prop
  ; ext_spec_post: forall e: E,
    ext_spec_type e -> injective_PTree block -> option typ -> option val -> Z -> M ->  Prop
  ; ext_spec_exit: option val -> Z -> M ->  Prop }.Structure external_specification (M E Z : Type) :=
  { ext_spec_type : E -> Type
  ; ext_spec_pre: forall e: E,
    ext_spec_type e -> injective_PTree block -> list typ -> list val -> Z -> M -> Prop
  ; ext_spec_post: forall e: E,
    ext_spec_type e -> injective_PTree block -> option typ -> option val -> Z -> M ->  Prop
  ; ext_spec_exit: option val -> Z -> M ->  Prop }.Structure external_specification (M E Z : Type) :=
  { ext_spec_type : E -> Type
  ; ext_spec_pre: forall e: E,
    ext_spec_type e -> injective_PTree block -> list typ -> list val -> Z -> M -> Prop
  ; ext_spec_post: forall e: E,
    ext_spec_type e -> injective_PTree block -> option typ -> option val -> Z -> M ->  Prop
  ; ext_spec_exit: option val -> Z -> M ->  Prop }.Structure external_specification (M E Z : Type) :=
  { ext_spec_type : E -> Type
  ; ext_spec_pre: forall e: E,
    ext_spec_type e -> injective_PTree block -> list typ -> list val -> Z -> M -> Prop
  ; ext_spec_post: forall e: E,
    ext_spec_type e -> injective_PTree block -> option typ -> option val -> Z -> M ->  Prop
  ; ext_spec_exit: option val -> Z -> M ->  Prop }.Definition ext_spec := external_specification mem external_function.

(* Specifications: *)
Lemma extfunct_eqdec (ef1 ef2 : external_function) : {ef1=ef2} + {~ef1=ef2}.