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Code-segment-descriptor-attributesbits

Code-segment-descriptor-attributesbits-fix

Fixing function for code-segment-descriptor-attributesbits bit structures.

Signature
(code-segment-descriptor-attributesbits-fix x) → fty::fixed
Arguments: x — Guard (code-segment-descriptor-attributesbits-p x).
Returns: fty::fixed — Type (code-segment-descriptor-attributesbits-p fty::fixed).

Definitions and Theorems

Function: code-segment-descriptor-attributesbits-fix

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

Theorem: code-segment-descriptor-attributesbits-p-of-code-segment-descriptor-attributesbits-fix

(defthm
 code-segment-descriptor-attributesbits-p-of-code-segment-descriptor-attributesbits-fix
 (b* ((fty::fixed (code-segment-descriptor-attributesbits-fix x)))
   (code-segment-descriptor-attributesbits-p fty::fixed))
 :rule-classes :rewrite)

Theorem: code-segment-descriptor-attributesbits-fix-when-code-segment-descriptor-attributesbits-p

(defthm
 code-segment-descriptor-attributesbits-fix-when-code-segment-descriptor-attributesbits-p
 (implies (code-segment-descriptor-attributesbits-p x)
          (equal (code-segment-descriptor-attributesbits-fix x)
                 x)))

Function: code-segment-descriptor-attributesbits-equiv$inline

(defun code-segment-descriptor-attributesbits-equiv$inline (x y)
 (declare
  (xargs :guard (and (code-segment-descriptor-attributesbits-p x)
                     (code-segment-descriptor-attributesbits-p y))))
 (equal (code-segment-descriptor-attributesbits-fix x)
        (code-segment-descriptor-attributesbits-fix y)))

Theorem: code-segment-descriptor-attributesbits-equiv-is-an-equivalence

(defthm
     code-segment-descriptor-attributesbits-equiv-is-an-equivalence
 (and
   (booleanp (code-segment-descriptor-attributesbits-equiv x y))
   (code-segment-descriptor-attributesbits-equiv x x)
   (implies (code-segment-descriptor-attributesbits-equiv x y)
            (code-segment-descriptor-attributesbits-equiv y x))
   (implies (and (code-segment-descriptor-attributesbits-equiv x y)
                 (code-segment-descriptor-attributesbits-equiv y z))
            (code-segment-descriptor-attributesbits-equiv x z)))
 :rule-classes (:equivalence))

Theorem: code-segment-descriptor-attributesbits-equiv-implies-equal-code-segment-descriptor-attributesbits-fix-1

(defthm
 code-segment-descriptor-attributesbits-equiv-implies-equal-code-segment-descriptor-attributesbits-fix-1
 (implies
      (code-segment-descriptor-attributesbits-equiv x x-equiv)
      (equal (code-segment-descriptor-attributesbits-fix x)
             (code-segment-descriptor-attributesbits-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: code-segment-descriptor-attributesbits-fix-under-code-segment-descriptor-attributesbits-equiv

(defthm
 code-segment-descriptor-attributesbits-fix-under-code-segment-descriptor-attributesbits-equiv
 (code-segment-descriptor-attributesbits-equiv
      (code-segment-descriptor-attributesbits-fix x)
      x)
 :rule-classes (:rewrite :rewrite-quoted-constant))