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Elf_bits8

Elf_bits8-fix

Fixing function for elf_bits8 bit structures.

Signature
(elf_bits8-fix x) → fty::fixed
Arguments: x — Guard (elf_bits8-p x).
Returns: fty::fixed — Type (elf_bits8-p fty::fixed).

Definitions and Theorems

Function: elf_bits8-fix

(defun elf_bits8-fix (x)
  (declare (xargs :guard (elf_bits8-p x)))
  (let ((__function__ 'elf_bits8-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 8 x) :exec x)))

Theorem: elf_bits8-p-of-elf_bits8-fix

(defthm elf_bits8-p-of-elf_bits8-fix
  (b* ((fty::fixed (elf_bits8-fix x)))
    (elf_bits8-p fty::fixed))
  :rule-classes :rewrite)

Theorem: elf_bits8-fix-when-elf_bits8-p

(defthm elf_bits8-fix-when-elf_bits8-p
  (implies (elf_bits8-p x)
           (equal (elf_bits8-fix x) x)))

Function: elf_bits8-equiv$inline

(defun elf_bits8-equiv$inline (x y)
  (declare (xargs :guard (and (elf_bits8-p x) (elf_bits8-p y))))
  (equal (elf_bits8-fix x)
         (elf_bits8-fix y)))

Theorem: elf_bits8-equiv-is-an-equivalence

(defthm elf_bits8-equiv-is-an-equivalence
  (and (booleanp (elf_bits8-equiv x y))
       (elf_bits8-equiv x x)
       (implies (elf_bits8-equiv x y)
                (elf_bits8-equiv y x))
       (implies (and (elf_bits8-equiv x y)
                     (elf_bits8-equiv y z))
                (elf_bits8-equiv x z)))
  :rule-classes (:equivalence))

Theorem: elf_bits8-equiv-implies-equal-elf_bits8-fix-1

(defthm elf_bits8-equiv-implies-equal-elf_bits8-fix-1
  (implies (elf_bits8-equiv x x-equiv)
           (equal (elf_bits8-fix x)
                  (elf_bits8-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: elf_bits8-fix-under-elf_bits8-equiv

(defthm elf_bits8-fix-under-elf_bits8-equiv
  (elf_bits8-equiv (elf_bits8-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))