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• Elf32-segment-header

Elf32-segment-header-fix

Fixing function for elf32-segment-header structures.

Signature

(elf32-segment-header-fix x) → new-x

Arguments

x — Guard (elf32-segment-header-p x).

Returns

new-x — Type (elf32-segment-header-p new-x).

Definitions and Theorems

Function: elf32-segment-header-fix$inline

(defun elf32-segment-header-fix$inline (x)
  (declare (xargs :guard (elf32-segment-header-p x)))
  (let ((__function__ 'elf32-segment-header-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((type (nfix (cdr (std::da-nth 0 x))))
              (flags (nfix (cdr (std::da-nth 1 x))))
              (offset (nfix (cdr (std::da-nth 2 x))))
              (vaddr (nfix (cdr (std::da-nth 3 x))))
              (paddr (nfix (cdr (std::da-nth 4 x))))
              (filesz (nfix (cdr (std::da-nth 5 x))))
              (memsz (nfix (cdr (std::da-nth 6 x))))
              (align (nfix (cdr (std::da-nth 7 x)))))
           (list (cons 'type type)
                 (cons 'flags flags)
                 (cons 'offset offset)
                 (cons 'vaddr vaddr)
                 (cons 'paddr paddr)
                 (cons 'filesz filesz)
                 (cons 'memsz memsz)
                 (cons 'align align)))
         :exec x)))

Theorem: elf32-segment-header-p-of-elf32-segment-header-fix

(defthm elf32-segment-header-p-of-elf32-segment-header-fix
  (b* ((new-x (elf32-segment-header-fix$inline x)))
    (elf32-segment-header-p new-x))
  :rule-classes :rewrite)

Theorem: elf32-segment-header-fix-when-elf32-segment-header-p

(defthm elf32-segment-header-fix-when-elf32-segment-header-p
  (implies (elf32-segment-header-p x)
           (equal (elf32-segment-header-fix x) x)))

Function: elf32-segment-header-equiv$inline

(defun elf32-segment-header-equiv$inline (x y)
  (declare (xargs :guard (and (elf32-segment-header-p x)
                              (elf32-segment-header-p y))))
  (equal (elf32-segment-header-fix x)
         (elf32-segment-header-fix y)))

Theorem: elf32-segment-header-equiv-is-an-equivalence

(defthm elf32-segment-header-equiv-is-an-equivalence
  (and (booleanp (elf32-segment-header-equiv x y))
       (elf32-segment-header-equiv x x)
       (implies (elf32-segment-header-equiv x y)
                (elf32-segment-header-equiv y x))
       (implies (and (elf32-segment-header-equiv x y)
                     (elf32-segment-header-equiv y z))
                (elf32-segment-header-equiv x z)))
  :rule-classes (:equivalence))

Theorem: elf32-segment-header-equiv-implies-equal-elf32-segment-header-fix-1

(defthm
 elf32-segment-header-equiv-implies-equal-elf32-segment-header-fix-1
 (implies (elf32-segment-header-equiv x x-equiv)
          (equal (elf32-segment-header-fix x)
                 (elf32-segment-header-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: elf32-segment-header-fix-under-elf32-segment-header-equiv

(defthm elf32-segment-header-fix-under-elf32-segment-header-equiv
  (elf32-segment-header-equiv (elf32-segment-header-fix x)
                              x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-elf32-segment-header-fix-1-forward-to-elf32-segment-header-equiv

(defthm
 equal-of-elf32-segment-header-fix-1-forward-to-elf32-segment-header-equiv
 (implies (equal (elf32-segment-header-fix x) y)
          (elf32-segment-header-equiv x y))
 :rule-classes :forward-chaining)

Theorem: equal-of-elf32-segment-header-fix-2-forward-to-elf32-segment-header-equiv

(defthm
 equal-of-elf32-segment-header-fix-2-forward-to-elf32-segment-header-equiv
 (implies (equal x (elf32-segment-header-fix y))
          (elf32-segment-header-equiv x y))
 :rule-classes :forward-chaining)

Theorem: elf32-segment-header-equiv-of-elf32-segment-header-fix-1-forward

(defthm
   elf32-segment-header-equiv-of-elf32-segment-header-fix-1-forward
  (implies (elf32-segment-header-equiv (elf32-segment-header-fix x)
                                       y)
           (elf32-segment-header-equiv x y))
  :rule-classes :forward-chaining)

Theorem: elf32-segment-header-equiv-of-elf32-segment-header-fix-2-forward

(defthm
   elf32-segment-header-equiv-of-elf32-segment-header-fix-2-forward
  (implies
       (elf32-segment-header-equiv x (elf32-segment-header-fix y))
       (elf32-segment-header-equiv x y))
  :rule-classes :forward-chaining)