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Elf64_sym

Elf64_sym-fix

Fixing function for elf64_sym bit structures.

Signature
(elf64_sym-fix x) → fty::fixed
Arguments: x — Guard (elf64_sym-p x).
Returns: fty::fixed — Type (elf64_sym-p fty::fixed).

Definitions and Theorems

Function: elf64_sym-fix

(defun elf64_sym-fix (x)
  (declare (xargs :guard (elf64_sym-p x)))
  (let ((__function__ 'elf64_sym-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 192 x) :exec x)))

Theorem: elf64_sym-p-of-elf64_sym-fix

(defthm elf64_sym-p-of-elf64_sym-fix
  (b* ((fty::fixed (elf64_sym-fix x)))
    (elf64_sym-p fty::fixed))
  :rule-classes :rewrite)

Theorem: elf64_sym-fix-when-elf64_sym-p

(defthm elf64_sym-fix-when-elf64_sym-p
  (implies (elf64_sym-p x)
           (equal (elf64_sym-fix x) x)))

Function: elf64_sym-equiv$inline

(defun elf64_sym-equiv$inline (x y)
  (declare (xargs :guard (and (elf64_sym-p x) (elf64_sym-p y))))
  (equal (elf64_sym-fix x)
         (elf64_sym-fix y)))

Theorem: elf64_sym-equiv-is-an-equivalence

(defthm elf64_sym-equiv-is-an-equivalence
  (and (booleanp (elf64_sym-equiv x y))
       (elf64_sym-equiv x x)
       (implies (elf64_sym-equiv x y)
                (elf64_sym-equiv y x))
       (implies (and (elf64_sym-equiv x y)
                     (elf64_sym-equiv y z))
                (elf64_sym-equiv x z)))
  :rule-classes (:equivalence))

Theorem: elf64_sym-equiv-implies-equal-elf64_sym-fix-1

(defthm elf64_sym-equiv-implies-equal-elf64_sym-fix-1
  (implies (elf64_sym-equiv x x-equiv)
           (equal (elf64_sym-fix x)
                  (elf64_sym-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: elf64_sym-fix-under-elf64_sym-equiv

(defthm elf64_sym-fix-under-elf64_sym-equiv
  (elf64_sym-equiv (elf64_sym-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))