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• Mach-o-section-header

Mach-o-section-header-fix

Fixing function for mach-o-section-header structures.

Signature

(mach-o-section-header-fix x) → new-x

Arguments

x — Guard (mach-o-section-header-p x).

Returns

new-x — Type (mach-o-section-header-p new-x).

Definitions and Theorems

Function: mach-o-section-header-fix$inline

(defun mach-o-section-header-fix$inline (x)
  (declare (xargs :guard (mach-o-section-header-p x)))
  (let ((__function__ 'mach-o-section-header-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((sectname (acl2::str-fix (cdr (std::da-nth 0 x))))
              (segname (acl2::str-fix (cdr (std::da-nth 1 x))))
              (addr (nfix (cdr (std::da-nth 2 x))))
              (size (nfix (cdr (std::da-nth 3 x))))
              (offset (nfix (cdr (std::da-nth 4 x))))
              (align (nfix (cdr (std::da-nth 5 x))))
              (reloff (nfix (cdr (std::da-nth 6 x))))
              (nreloc (nfix (cdr (std::da-nth 7 x))))
              (flags (nfix (cdr (std::da-nth 8 x))))
              (reserved1 (nfix (cdr (std::da-nth 9 x))))
              (reserved2 (nfix (cdr (std::da-nth 10 x))))
              (reserved3 (nfix (cdr (std::da-nth 11 x)))))
           (list (cons 'sectname sectname)
                 (cons 'segname segname)
                 (cons 'addr addr)
                 (cons 'size size)
                 (cons 'offset offset)
                 (cons 'align align)
                 (cons 'reloff reloff)
                 (cons 'nreloc nreloc)
                 (cons 'flags flags)
                 (cons 'reserved1 reserved1)
                 (cons 'reserved2 reserved2)
                 (cons 'reserved3 reserved3)))
         :exec x)))

Theorem: mach-o-section-header-p-of-mach-o-section-header-fix

(defthm mach-o-section-header-p-of-mach-o-section-header-fix
  (b* ((new-x (mach-o-section-header-fix$inline x)))
    (mach-o-section-header-p new-x))
  :rule-classes :rewrite)

Theorem: mach-o-section-header-fix-when-mach-o-section-header-p

(defthm mach-o-section-header-fix-when-mach-o-section-header-p
  (implies (mach-o-section-header-p x)
           (equal (mach-o-section-header-fix x)
                  x)))

Function: mach-o-section-header-equiv$inline

(defun mach-o-section-header-equiv$inline (x y)
  (declare (xargs :guard (and (mach-o-section-header-p x)
                              (mach-o-section-header-p y))))
  (equal (mach-o-section-header-fix x)
         (mach-o-section-header-fix y)))

Theorem: mach-o-section-header-equiv-is-an-equivalence

(defthm mach-o-section-header-equiv-is-an-equivalence
  (and (booleanp (mach-o-section-header-equiv x y))
       (mach-o-section-header-equiv x x)
       (implies (mach-o-section-header-equiv x y)
                (mach-o-section-header-equiv y x))
       (implies (and (mach-o-section-header-equiv x y)
                     (mach-o-section-header-equiv y z))
                (mach-o-section-header-equiv x z)))
  :rule-classes (:equivalence))

Theorem: mach-o-section-header-equiv-implies-equal-mach-o-section-header-fix-1

(defthm
 mach-o-section-header-equiv-implies-equal-mach-o-section-header-fix-1
 (implies (mach-o-section-header-equiv x x-equiv)
          (equal (mach-o-section-header-fix x)
                 (mach-o-section-header-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: mach-o-section-header-fix-under-mach-o-section-header-equiv

(defthm mach-o-section-header-fix-under-mach-o-section-header-equiv
  (mach-o-section-header-equiv (mach-o-section-header-fix x)
                               x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-mach-o-section-header-fix-1-forward-to-mach-o-section-header-equiv

(defthm
 equal-of-mach-o-section-header-fix-1-forward-to-mach-o-section-header-equiv
 (implies (equal (mach-o-section-header-fix x) y)
          (mach-o-section-header-equiv x y))
 :rule-classes :forward-chaining)

Theorem: equal-of-mach-o-section-header-fix-2-forward-to-mach-o-section-header-equiv

(defthm
 equal-of-mach-o-section-header-fix-2-forward-to-mach-o-section-header-equiv
 (implies (equal x (mach-o-section-header-fix y))
          (mach-o-section-header-equiv x y))
 :rule-classes :forward-chaining)

Theorem: mach-o-section-header-equiv-of-mach-o-section-header-fix-1-forward

(defthm
 mach-o-section-header-equiv-of-mach-o-section-header-fix-1-forward
 (implies (mach-o-section-header-equiv (mach-o-section-header-fix x)
                                       y)
          (mach-o-section-header-equiv x y))
 :rule-classes :forward-chaining)

Theorem: mach-o-section-header-equiv-of-mach-o-section-header-fix-2-forward

(defthm
 mach-o-section-header-equiv-of-mach-o-section-header-fix-2-forward
 (implies
      (mach-o-section-header-equiv x (mach-o-section-header-fix y))
      (mach-o-section-header-equiv x y))
 :rule-classes :forward-chaining)