		Search-engine friendly clone of the ACL2 documentation.

Extdecl

Extdecl-fix

Fixing function for extdecl structures.

Signature
(extdecl-fix x) → new-x
Arguments: x — Guard (extdeclp x).
Returns: new-x — Type (extdeclp new-x).

Definitions and Theorems

Function: extdecl-fix$inline

(defun extdecl-fix$inline (x)
 (declare (xargs :guard (extdeclp x)))
 (let ((__function__ 'extdecl-fix))
  (declare (ignorable __function__))
  (mbe
      :logic
      (case (extdecl-kind x)
        (:fundef (b* ((unwrap (fundef-fix (std::da-nth 0 (cdr x)))))
                   (cons :fundef (list unwrap))))
        (:decl (b* ((unwrap (decl-fix (std::da-nth 0 (cdr x)))))
                 (cons :decl (list unwrap))))
        (:empty (cons :empty (list)))
        (:asm (b* ((unwrap (asm-stmt-fix (std::da-nth 0 (cdr x)))))
                (cons :asm (list unwrap)))))
      :exec x)))

Theorem: extdeclp-of-extdecl-fix

(defthm extdeclp-of-extdecl-fix
  (b* ((new-x (extdecl-fix$inline x)))
    (extdeclp new-x))
  :rule-classes :rewrite)

Theorem: extdecl-fix-when-extdeclp

(defthm extdecl-fix-when-extdeclp
  (implies (extdeclp x)
           (equal (extdecl-fix x) x)))

Function: extdecl-equiv$inline

(defun extdecl-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (extdeclp acl2::x)
                              (extdeclp acl2::y))))
  (equal (extdecl-fix acl2::x)
         (extdecl-fix acl2::y)))

Theorem: extdecl-equiv-is-an-equivalence

(defthm extdecl-equiv-is-an-equivalence
  (and (booleanp (extdecl-equiv x y))
       (extdecl-equiv x x)
       (implies (extdecl-equiv x y)
                (extdecl-equiv y x))
       (implies (and (extdecl-equiv x y)
                     (extdecl-equiv y z))
                (extdecl-equiv x z)))
  :rule-classes (:equivalence))

Theorem: extdecl-equiv-implies-equal-extdecl-fix-1

(defthm extdecl-equiv-implies-equal-extdecl-fix-1
  (implies (extdecl-equiv acl2::x x-equiv)
           (equal (extdecl-fix acl2::x)
                  (extdecl-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: extdecl-fix-under-extdecl-equiv

(defthm extdecl-fix-under-extdecl-equiv
  (extdecl-equiv (extdecl-fix acl2::x)
                 acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-extdecl-fix-1-forward-to-extdecl-equiv

(defthm equal-of-extdecl-fix-1-forward-to-extdecl-equiv
  (implies (equal (extdecl-fix acl2::x) acl2::y)
           (extdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-extdecl-fix-2-forward-to-extdecl-equiv

(defthm equal-of-extdecl-fix-2-forward-to-extdecl-equiv
  (implies (equal acl2::x (extdecl-fix acl2::y))
           (extdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: extdecl-equiv-of-extdecl-fix-1-forward

(defthm extdecl-equiv-of-extdecl-fix-1-forward
  (implies (extdecl-equiv (extdecl-fix acl2::x)
                          acl2::y)
           (extdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: extdecl-equiv-of-extdecl-fix-2-forward

(defthm extdecl-equiv-of-extdecl-fix-2-forward
  (implies (extdecl-equiv acl2::x (extdecl-fix acl2::y))
           (extdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: extdecl-kind$inline-of-extdecl-fix-x

(defthm extdecl-kind$inline-of-extdecl-fix-x
  (equal (extdecl-kind$inline (extdecl-fix x))
         (extdecl-kind$inline x)))

Theorem: extdecl-kind$inline-extdecl-equiv-congruence-on-x

(defthm extdecl-kind$inline-extdecl-equiv-congruence-on-x
  (implies (extdecl-equiv x x-equiv)
           (equal (extdecl-kind$inline x)
                  (extdecl-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-extdecl-fix

(defthm consp-of-extdecl-fix
  (consp (extdecl-fix x))
  :rule-classes :type-prescription)