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Ia32e-pml4ebits

!ia32e-pml4ebits->res1

Update the |X86ISA|::|RES1| field of a ia32e-pml4ebits bit structure.

Signature
(!ia32e-pml4ebits->res1 res1 x) → new-x
Arguments: res1 — Guard (bitp res1).; x — Guard (ia32e-pml4ebits-p x).
Returns: new-x — Type (ia32e-pml4ebits-p new-x).

Definitions and Theorems

Function: !ia32e-pml4ebits->res1$inline

(defun !ia32e-pml4ebits->res1$inline (res1 x)
  (declare (xargs :guard (and (bitp res1)
                              (ia32e-pml4ebits-p x))))
  (mbe :logic
       (b* ((res1 (mbe :logic (bfix res1) :exec res1))
            (x (ia32e-pml4ebits-fix x)))
         (part-install res1 x :width 1 :low 6))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 8) -65)))
                          (the (unsigned-byte 7)
                               (ash (the (unsigned-byte 1) res1)
                                    6))))))

Theorem: ia32e-pml4ebits-p-of-!ia32e-pml4ebits->res1

(defthm ia32e-pml4ebits-p-of-!ia32e-pml4ebits->res1
  (b* ((new-x (!ia32e-pml4ebits->res1$inline res1 x)))
    (ia32e-pml4ebits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-pml4ebits->res1$inline-of-bfix-res1

(defthm !ia32e-pml4ebits->res1$inline-of-bfix-res1
  (equal (!ia32e-pml4ebits->res1$inline (bfix res1)
                                        x)
         (!ia32e-pml4ebits->res1$inline res1 x)))

Theorem: !ia32e-pml4ebits->res1$inline-bit-equiv-congruence-on-res1

(defthm !ia32e-pml4ebits->res1$inline-bit-equiv-congruence-on-res1
  (implies (bit-equiv res1 res1-equiv)
           (equal (!ia32e-pml4ebits->res1$inline res1 x)
                  (!ia32e-pml4ebits->res1$inline res1-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->res1$inline-of-ia32e-pml4ebits-fix-x

(defthm !ia32e-pml4ebits->res1$inline-of-ia32e-pml4ebits-fix-x
 (equal (!ia32e-pml4ebits->res1$inline res1 (ia32e-pml4ebits-fix x))
        (!ia32e-pml4ebits->res1$inline res1 x)))

Theorem: !ia32e-pml4ebits->res1$inline-ia32e-pml4ebits-equiv-congruence-on-x

(defthm
 !ia32e-pml4ebits->res1$inline-ia32e-pml4ebits-equiv-congruence-on-x
 (implies (ia32e-pml4ebits-equiv x x-equiv)
          (equal (!ia32e-pml4ebits->res1$inline res1 x)
                 (!ia32e-pml4ebits->res1$inline res1 x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->res1-is-ia32e-pml4ebits

(defthm !ia32e-pml4ebits->res1-is-ia32e-pml4ebits
  (equal (!ia32e-pml4ebits->res1 res1 x)
         (change-ia32e-pml4ebits x :res1 res1)))

Theorem: ia32e-pml4ebits->res1-of-!ia32e-pml4ebits->res1

(defthm ia32e-pml4ebits->res1-of-!ia32e-pml4ebits->res1
  (b* ((?new-x (!ia32e-pml4ebits->res1$inline res1 x)))
    (equal (ia32e-pml4ebits->res1 new-x)
           (bfix res1))))

Theorem: !ia32e-pml4ebits->res1-equiv-under-mask

(defthm !ia32e-pml4ebits->res1-equiv-under-mask
  (b* ((?new-x (!ia32e-pml4ebits->res1$inline res1 x)))
    (ia32e-pml4ebits-equiv-under-mask new-x x -65)))