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Vex3-byte1

!vex3-byte1->m-mmmm

Update the |X86ISA|::|M-MMMM| field of a vex3-byte1 bit structure.

Signature
(!vex3-byte1->m-mmmm m-mmmm vex3byte1) → new-vex3byte1
Arguments: m-mmmm — Guard (5bits-p m-mmmm).; vex3byte1 — Guard (vex3-byte1-p vex3byte1).
Returns: new-vex3byte1 — Type (vex3-byte1-p new-vex3byte1).

Definitions and Theorems

Function: !vex3-byte1->m-mmmm$inline

(defun !vex3-byte1->m-mmmm$inline (m-mmmm vex3byte1)
 (declare (xargs :guard (and (5bits-p m-mmmm)
                             (vex3-byte1-p vex3byte1))))
 (mbe
   :logic
   (b* ((m-mmmm (mbe :logic (5bits-fix m-mmmm)
                     :exec m-mmmm))
        (vex3byte1 (vex3-byte1-fix vex3byte1)))
     (part-install m-mmmm vex3byte1
                   :width 5
                   :low 0))
   :exec (the (unsigned-byte 8)
              (logior (the (unsigned-byte 8)
                           (logand (the (unsigned-byte 8) vex3byte1)
                                   (the (signed-byte 6) -32)))
                      (the (unsigned-byte 5) m-mmmm)))))

Theorem: vex3-byte1-p-of-!vex3-byte1->m-mmmm

(defthm vex3-byte1-p-of-!vex3-byte1->m-mmmm
 (b* ((new-vex3byte1 (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))
   (vex3-byte1-p new-vex3byte1))
 :rule-classes :rewrite)

Theorem: !vex3-byte1->m-mmmm$inline-of-5bits-fix-m-mmmm

(defthm !vex3-byte1->m-mmmm$inline-of-5bits-fix-m-mmmm
  (equal (!vex3-byte1->m-mmmm$inline (5bits-fix m-mmmm)
                                     vex3byte1)
         (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))

Theorem: !vex3-byte1->m-mmmm$inline-5bits-equiv-congruence-on-m-mmmm

(defthm !vex3-byte1->m-mmmm$inline-5bits-equiv-congruence-on-m-mmmm
  (implies
       (5bits-equiv m-mmmm m-mmmm-equiv)
       (equal (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)
              (!vex3-byte1->m-mmmm$inline m-mmmm-equiv vex3byte1)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->m-mmmm$inline-of-vex3-byte1-fix-vex3byte1

(defthm !vex3-byte1->m-mmmm$inline-of-vex3-byte1-fix-vex3byte1
 (equal
      (!vex3-byte1->m-mmmm$inline m-mmmm (vex3-byte1-fix vex3byte1))
      (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))

Theorem: !vex3-byte1->m-mmmm$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
 !vex3-byte1->m-mmmm$inline-vex3-byte1-equiv-congruence-on-vex3byte1
 (implies
      (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
      (equal (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)
             (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1-equiv)))
 :rule-classes :congruence)

Theorem: !vex3-byte1->m-mmmm-is-vex3-byte1

(defthm !vex3-byte1->m-mmmm-is-vex3-byte1
  (equal (!vex3-byte1->m-mmmm m-mmmm vex3byte1)
         (change-vex3-byte1 vex3byte1
                            :m-mmmm m-mmmm)))

Theorem: vex3-byte1->m-mmmm-of-!vex3-byte1->m-mmmm

(defthm vex3-byte1->m-mmmm-of-!vex3-byte1->m-mmmm
  (b*
    ((?new-vex3byte1 (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))
    (equal (vex3-byte1->m-mmmm new-vex3byte1)
           (5bits-fix m-mmmm))))

Theorem: !vex3-byte1->m-mmmm-equiv-under-mask

(defthm !vex3-byte1->m-mmmm-equiv-under-mask
  (b*
    ((?new-vex3byte1 (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))
    (vex3-byte1-equiv-under-mask new-vex3byte1 vex3byte1 -32)))