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  • Math
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• Elf32_sym-info

Elf32_sym-info-fix

Fixing function for elf32_sym-info structures.

Signature

(elf32_sym-info-fix x) → new-x

Arguments

x — Guard (elf32_sym-info-p x).

Returns

new-x — Type (elf32_sym-info-p new-x).

Definitions and Theorems

Function: elf32_sym-info-fix$inline

(defun elf32_sym-info-fix$inline (x)
  (declare (xargs :guard (elf32_sym-info-p x)))
  (let ((__function__ 'elf32_sym-info-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name-str (acl2::str-fix (cdr (std::da-nth 0 x))))
              (entry (elf32_sym-fix (cdr (std::da-nth 1 x)))))
           (list (cons 'name-str name-str)
                 (cons 'entry entry)))
         :exec x)))

Theorem: elf32_sym-info-p-of-elf32_sym-info-fix

(defthm elf32_sym-info-p-of-elf32_sym-info-fix
  (b* ((new-x (elf32_sym-info-fix$inline x)))
    (elf32_sym-info-p new-x))
  :rule-classes :rewrite)

Theorem: elf32_sym-info-fix-when-elf32_sym-info-p

(defthm elf32_sym-info-fix-when-elf32_sym-info-p
  (implies (elf32_sym-info-p x)
           (equal (elf32_sym-info-fix x) x)))

Function: elf32_sym-info-equiv$inline

(defun elf32_sym-info-equiv$inline (x y)
  (declare (xargs :guard (and (elf32_sym-info-p x)
                              (elf32_sym-info-p y))))
  (equal (elf32_sym-info-fix x)
         (elf32_sym-info-fix y)))

Theorem: elf32_sym-info-equiv-is-an-equivalence

(defthm elf32_sym-info-equiv-is-an-equivalence
  (and (booleanp (elf32_sym-info-equiv x y))
       (elf32_sym-info-equiv x x)
       (implies (elf32_sym-info-equiv x y)
                (elf32_sym-info-equiv y x))
       (implies (and (elf32_sym-info-equiv x y)
                     (elf32_sym-info-equiv y z))
                (elf32_sym-info-equiv x z)))
  :rule-classes (:equivalence))

Theorem: elf32_sym-info-equiv-implies-equal-elf32_sym-info-fix-1

(defthm elf32_sym-info-equiv-implies-equal-elf32_sym-info-fix-1
  (implies (elf32_sym-info-equiv x x-equiv)
           (equal (elf32_sym-info-fix x)
                  (elf32_sym-info-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: elf32_sym-info-fix-under-elf32_sym-info-equiv

(defthm elf32_sym-info-fix-under-elf32_sym-info-equiv
  (elf32_sym-info-equiv (elf32_sym-info-fix x)
                        x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-elf32_sym-info-fix-1-forward-to-elf32_sym-info-equiv

(defthm
      equal-of-elf32_sym-info-fix-1-forward-to-elf32_sym-info-equiv
  (implies (equal (elf32_sym-info-fix x) y)
           (elf32_sym-info-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-elf32_sym-info-fix-2-forward-to-elf32_sym-info-equiv

(defthm
      equal-of-elf32_sym-info-fix-2-forward-to-elf32_sym-info-equiv
  (implies (equal x (elf32_sym-info-fix y))
           (elf32_sym-info-equiv x y))
  :rule-classes :forward-chaining)

Theorem: elf32_sym-info-equiv-of-elf32_sym-info-fix-1-forward

(defthm elf32_sym-info-equiv-of-elf32_sym-info-fix-1-forward
  (implies (elf32_sym-info-equiv (elf32_sym-info-fix x)
                                 y)
           (elf32_sym-info-equiv x y))
  :rule-classes :forward-chaining)

Theorem: elf32_sym-info-equiv-of-elf32_sym-info-fix-2-forward

(defthm elf32_sym-info-equiv-of-elf32_sym-info-fix-2-forward
  (implies (elf32_sym-info-equiv x (elf32_sym-info-fix y))
           (elf32_sym-info-equiv x y))
  :rule-classes :forward-chaining)