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Evex-byte1

Evex-byte1-fix

Fixing function for evex-byte1 bit structures.

Signature
(evex-byte1-fix byte1) → fty::fixed
Arguments: byte1 — Guard (evex-byte1-p byte1).
Returns: fty::fixed — Type (evex-byte1-p fty::fixed).

Definitions and Theorems

Function: evex-byte1-fix$inline

(defun evex-byte1-fix$inline (byte1)
  (declare (xargs :guard (evex-byte1-p byte1)))
  (mbe :logic (loghead 8 byte1)
       :exec byte1))

Theorem: evex-byte1-p-of-evex-byte1-fix

(defthm evex-byte1-p-of-evex-byte1-fix
  (b* ((fty::fixed (evex-byte1-fix$inline byte1)))
    (evex-byte1-p fty::fixed))
  :rule-classes :rewrite)

Theorem: evex-byte1-fix-when-evex-byte1-p

(defthm evex-byte1-fix-when-evex-byte1-p
  (implies (evex-byte1-p byte1)
           (equal (evex-byte1-fix byte1) byte1)))

Function: evex-byte1-equiv$inline

(defun evex-byte1-equiv$inline (x y)
  (declare (xargs :guard (and (evex-byte1-p x)
                              (evex-byte1-p y))))
  (equal (evex-byte1-fix x)
         (evex-byte1-fix y)))

Theorem: evex-byte1-equiv-is-an-equivalence

(defthm evex-byte1-equiv-is-an-equivalence
  (and (booleanp (evex-byte1-equiv x y))
       (evex-byte1-equiv x x)
       (implies (evex-byte1-equiv x y)
                (evex-byte1-equiv y x))
       (implies (and (evex-byte1-equiv x y)
                     (evex-byte1-equiv y z))
                (evex-byte1-equiv x z)))
  :rule-classes (:equivalence))

Theorem: evex-byte1-equiv-implies-equal-evex-byte1-fix-1

(defthm evex-byte1-equiv-implies-equal-evex-byte1-fix-1
  (implies (evex-byte1-equiv x x-equiv)
           (equal (evex-byte1-fix x)
                  (evex-byte1-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: evex-byte1-fix-under-evex-byte1-equiv

(defthm evex-byte1-fix-under-evex-byte1-equiv
  (evex-byte1-equiv (evex-byte1-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))