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Elf_bits16

Elf_bits16-fix

Fixing function for elf_bits16 bit structures.

Signature
(elf_bits16-fix x) → fty::fixed
Arguments: x — Guard (elf_bits16-p x).
Returns: fty::fixed — Type (elf_bits16-p fty::fixed).

Definitions and Theorems

Function: elf_bits16-fix

(defun elf_bits16-fix (x)
  (declare (xargs :guard (elf_bits16-p x)))
  (let ((__function__ 'elf_bits16-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 16 x) :exec x)))

Theorem: elf_bits16-p-of-elf_bits16-fix

(defthm elf_bits16-p-of-elf_bits16-fix
  (b* ((fty::fixed (elf_bits16-fix x)))
    (elf_bits16-p fty::fixed))
  :rule-classes :rewrite)

Theorem: elf_bits16-fix-when-elf_bits16-p

(defthm elf_bits16-fix-when-elf_bits16-p
  (implies (elf_bits16-p x)
           (equal (elf_bits16-fix x) x)))

Function: elf_bits16-equiv$inline

(defun elf_bits16-equiv$inline (x y)
  (declare (xargs :guard (and (elf_bits16-p x)
                              (elf_bits16-p y))))
  (equal (elf_bits16-fix x)
         (elf_bits16-fix y)))

Theorem: elf_bits16-equiv-is-an-equivalence

(defthm elf_bits16-equiv-is-an-equivalence
  (and (booleanp (elf_bits16-equiv x y))
       (elf_bits16-equiv x x)
       (implies (elf_bits16-equiv x y)
                (elf_bits16-equiv y x))
       (implies (and (elf_bits16-equiv x y)
                     (elf_bits16-equiv y z))
                (elf_bits16-equiv x z)))
  :rule-classes (:equivalence))

Theorem: elf_bits16-equiv-implies-equal-elf_bits16-fix-1

(defthm elf_bits16-equiv-implies-equal-elf_bits16-fix-1
  (implies (elf_bits16-equiv x x-equiv)
           (equal (elf_bits16-fix x)
                  (elf_bits16-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: elf_bits16-fix-under-elf_bits16-equiv

(defthm elf_bits16-fix-under-elf_bits16-equiv
  (elf_bits16-equiv (elf_bits16-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))