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Ia32e-page-tablesbits

!ia32e-page-tablesbits->res1

Update the |X86ISA|::|RES1| field of a ia32e-page-tablesbits bit structure.

Signature
(!ia32e-page-tablesbits->res1 res1 x) → new-x
Arguments: res1 — Guard (4bits-p res1).; x — Guard (ia32e-page-tablesbits-p x).
Returns: new-x — Type (ia32e-page-tablesbits-p new-x).

Definitions and Theorems

Function: !ia32e-page-tablesbits->res1$inline

(defun !ia32e-page-tablesbits->res1$inline (res1 x)
 (declare (xargs :guard (and (4bits-p res1)
                             (ia32e-page-tablesbits-p x))))
 (mbe :logic
      (b* ((res1 (mbe :logic (4bits-fix res1)
                      :exec res1))
           (x (ia32e-page-tablesbits-fix x)))
        (part-install res1 x :width 4 :low 8))
      :exec (the (unsigned-byte 64)
                 (logior (the (unsigned-byte 64)
                              (logand (the (unsigned-byte 64) x)
                                      (the (signed-byte 13) -3841)))
                         (the (unsigned-byte 12)
                              (ash (the (unsigned-byte 4) res1)
                                   8))))))

Theorem: ia32e-page-tablesbits-p-of-!ia32e-page-tablesbits->res1

(defthm ia32e-page-tablesbits-p-of-!ia32e-page-tablesbits->res1
  (b* ((new-x (!ia32e-page-tablesbits->res1$inline res1 x)))
    (ia32e-page-tablesbits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-page-tablesbits->res1$inline-of-4bits-fix-res1

(defthm !ia32e-page-tablesbits->res1$inline-of-4bits-fix-res1
  (equal (!ia32e-page-tablesbits->res1$inline (4bits-fix res1)
                                              x)
         (!ia32e-page-tablesbits->res1$inline res1 x)))

Theorem: !ia32e-page-tablesbits->res1$inline-4bits-equiv-congruence-on-res1

(defthm
 !ia32e-page-tablesbits->res1$inline-4bits-equiv-congruence-on-res1
 (implies
      (4bits-equiv res1 res1-equiv)
      (equal (!ia32e-page-tablesbits->res1$inline res1 x)
             (!ia32e-page-tablesbits->res1$inline res1-equiv x)))
 :rule-classes :congruence)

Theorem: !ia32e-page-tablesbits->res1$inline-of-ia32e-page-tablesbits-fix-x

(defthm
 !ia32e-page-tablesbits->res1$inline-of-ia32e-page-tablesbits-fix-x
 (equal (!ia32e-page-tablesbits->res1$inline
             res1 (ia32e-page-tablesbits-fix x))
        (!ia32e-page-tablesbits->res1$inline res1 x)))

Theorem: !ia32e-page-tablesbits->res1$inline-ia32e-page-tablesbits-equiv-congruence-on-x

(defthm
 !ia32e-page-tablesbits->res1$inline-ia32e-page-tablesbits-equiv-congruence-on-x
 (implies
      (ia32e-page-tablesbits-equiv x x-equiv)
      (equal (!ia32e-page-tablesbits->res1$inline res1 x)
             (!ia32e-page-tablesbits->res1$inline res1 x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-page-tablesbits->res1-is-ia32e-page-tablesbits

(defthm !ia32e-page-tablesbits->res1-is-ia32e-page-tablesbits
  (equal (!ia32e-page-tablesbits->res1 res1 x)
         (change-ia32e-page-tablesbits x
                                       :res1 res1)))

Theorem: ia32e-page-tablesbits->res1-of-!ia32e-page-tablesbits->res1

(defthm ia32e-page-tablesbits->res1-of-!ia32e-page-tablesbits->res1
  (b* ((?new-x (!ia32e-page-tablesbits->res1$inline res1 x)))
    (equal (ia32e-page-tablesbits->res1 new-x)
           (4bits-fix res1))))

Theorem: !ia32e-page-tablesbits->res1-equiv-under-mask

(defthm !ia32e-page-tablesbits->res1-equiv-under-mask
  (b* ((?new-x (!ia32e-page-tablesbits->res1$inline res1 x)))
    (ia32e-page-tablesbits-equiv-under-mask new-x x -3841)))