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Evex-prefixes

Evex-prefixes-fix

Fixing function for evex-prefixes bit structures.

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

Definitions and Theorems

Function: evex-prefixes-fix$inline

(defun evex-prefixes-fix$inline (x)
  (declare (xargs :guard (evex-prefixes-p x)))
  (mbe :logic (loghead 32 x) :exec x))

Theorem: evex-prefixes-p-of-evex-prefixes-fix

(defthm evex-prefixes-p-of-evex-prefixes-fix
  (b* ((fty::fixed (evex-prefixes-fix$inline x)))
    (evex-prefixes-p fty::fixed))
  :rule-classes :rewrite)

Theorem: evex-prefixes-fix-when-evex-prefixes-p

(defthm evex-prefixes-fix-when-evex-prefixes-p
  (implies (evex-prefixes-p x)
           (equal (evex-prefixes-fix x) x)))

Function: evex-prefixes-equiv$inline

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

Theorem: evex-prefixes-equiv-is-an-equivalence

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

Theorem: evex-prefixes-equiv-implies-equal-evex-prefixes-fix-1

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

Theorem: evex-prefixes-fix-under-evex-prefixes-equiv

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