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Ia32e-pml4ebits

Ia32e-pml4ebits-fix

Fixing function for ia32e-pml4ebits bit structures.

Signature
(ia32e-pml4ebits-fix x) → fty::fixed
Arguments: x — Guard (ia32e-pml4ebits-p x).
Returns: fty::fixed — Type (ia32e-pml4ebits-p fty::fixed).

Definitions and Theorems

Function: ia32e-pml4ebits-fix

(defun ia32e-pml4ebits-fix (x)
  (declare (xargs :guard (ia32e-pml4ebits-p x)))
  (let ((__function__ 'ia32e-pml4ebits-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 64 x) :exec x)))

Theorem: ia32e-pml4ebits-p-of-ia32e-pml4ebits-fix

(defthm ia32e-pml4ebits-p-of-ia32e-pml4ebits-fix
  (b* ((fty::fixed (ia32e-pml4ebits-fix x)))
    (ia32e-pml4ebits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: ia32e-pml4ebits-fix-when-ia32e-pml4ebits-p

(defthm ia32e-pml4ebits-fix-when-ia32e-pml4ebits-p
  (implies (ia32e-pml4ebits-p x)
           (equal (ia32e-pml4ebits-fix x) x)))

Function: ia32e-pml4ebits-equiv$inline

(defun ia32e-pml4ebits-equiv$inline (x y)
  (declare (xargs :guard (and (ia32e-pml4ebits-p x)
                              (ia32e-pml4ebits-p y))))
  (equal (ia32e-pml4ebits-fix x)
         (ia32e-pml4ebits-fix y)))

Theorem: ia32e-pml4ebits-equiv-is-an-equivalence

(defthm ia32e-pml4ebits-equiv-is-an-equivalence
  (and (booleanp (ia32e-pml4ebits-equiv x y))
       (ia32e-pml4ebits-equiv x x)
       (implies (ia32e-pml4ebits-equiv x y)
                (ia32e-pml4ebits-equiv y x))
       (implies (and (ia32e-pml4ebits-equiv x y)
                     (ia32e-pml4ebits-equiv y z))
                (ia32e-pml4ebits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ia32e-pml4ebits-equiv-implies-equal-ia32e-pml4ebits-fix-1

(defthm ia32e-pml4ebits-equiv-implies-equal-ia32e-pml4ebits-fix-1
  (implies (ia32e-pml4ebits-equiv x x-equiv)
           (equal (ia32e-pml4ebits-fix x)
                  (ia32e-pml4ebits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ia32e-pml4ebits-fix-under-ia32e-pml4ebits-equiv

(defthm ia32e-pml4ebits-fix-under-ia32e-pml4ebits-equiv
  (ia32e-pml4ebits-equiv (ia32e-pml4ebits-fix x)
                         x)
  :rule-classes (:rewrite :rewrite-quoted-constant))