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Ia32_eferbits

!ia32_eferbits->sce

Update the |X86ISA|::|SCE| field of a ia32_eferbits bit structure.

Signature
(!ia32_eferbits->sce sce x) → new-x
Arguments: sce — Guard (bitp sce).; x — Guard (ia32_eferbits-p x).
Returns: new-x — Type (ia32_eferbits-p new-x).

Definitions and Theorems

Function: !ia32_eferbits->sce$inline

(defun !ia32_eferbits->sce$inline (sce x)
  (declare (xargs :guard (and (bitp sce) (ia32_eferbits-p x))))
  (mbe :logic
       (b* ((sce (mbe :logic (bfix sce) :exec sce))
            (x (ia32_eferbits-fix x)))
         (part-install sce x :width 1 :low 0))
       :exec (the (unsigned-byte 12)
                  (logior (the (unsigned-byte 12)
                               (logand (the (unsigned-byte 12) x)
                                       (the (signed-byte 2) -2)))
                          (the (unsigned-byte 1) sce)))))

Theorem: ia32_eferbits-p-of-!ia32_eferbits->sce

(defthm ia32_eferbits-p-of-!ia32_eferbits->sce
  (b* ((new-x (!ia32_eferbits->sce$inline sce x)))
    (ia32_eferbits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32_eferbits->sce$inline-of-bfix-sce

(defthm !ia32_eferbits->sce$inline-of-bfix-sce
  (equal (!ia32_eferbits->sce$inline (bfix sce)
                                     x)
         (!ia32_eferbits->sce$inline sce x)))

Theorem: !ia32_eferbits->sce$inline-bit-equiv-congruence-on-sce

(defthm !ia32_eferbits->sce$inline-bit-equiv-congruence-on-sce
  (implies (bit-equiv sce sce-equiv)
           (equal (!ia32_eferbits->sce$inline sce x)
                  (!ia32_eferbits->sce$inline sce-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32_eferbits->sce$inline-of-ia32_eferbits-fix-x

(defthm !ia32_eferbits->sce$inline-of-ia32_eferbits-fix-x
  (equal (!ia32_eferbits->sce$inline sce (ia32_eferbits-fix x))
         (!ia32_eferbits->sce$inline sce x)))

Theorem: !ia32_eferbits->sce$inline-ia32_eferbits-equiv-congruence-on-x

(defthm
     !ia32_eferbits->sce$inline-ia32_eferbits-equiv-congruence-on-x
  (implies (ia32_eferbits-equiv x x-equiv)
           (equal (!ia32_eferbits->sce$inline sce x)
                  (!ia32_eferbits->sce$inline sce x-equiv)))
  :rule-classes :congruence)

Theorem: !ia32_eferbits->sce-is-ia32_eferbits

(defthm !ia32_eferbits->sce-is-ia32_eferbits
  (equal (!ia32_eferbits->sce sce x)
         (change-ia32_eferbits x :sce sce)))

Theorem: ia32_eferbits->sce-of-!ia32_eferbits->sce

(defthm ia32_eferbits->sce-of-!ia32_eferbits->sce
  (b* ((?new-x (!ia32_eferbits->sce$inline sce x)))
    (equal (ia32_eferbits->sce new-x)
           (bfix sce))))

Theorem: !ia32_eferbits->sce-equiv-under-mask

(defthm !ia32_eferbits->sce-equiv-under-mask
  (b* ((?new-x (!ia32_eferbits->sce$inline sce x)))
    (ia32_eferbits-equiv-under-mask new-x x -2)))