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Rflagsbits

!rflagsbits->pf

Update the |ACL2|::|PF| field of a rflagsbits bit structure.

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

Definitions and Theorems

Function: !rflagsbits->pf$inline

(defun !rflagsbits->pf$inline (pf x)
 (declare (xargs :guard (and (bitp pf) (rflagsbits-p x))))
 (mbe
     :logic
     (b* ((pf (mbe :logic (bfix pf) :exec pf))
          (x (rflagsbits-fix x)))
       (part-install pf x :width 1 :low 2))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 4) -5)))
                        (the (unsigned-byte 3)
                             (ash (the (unsigned-byte 1) pf) 2))))))

Theorem: rflagsbits-p-of-!rflagsbits->pf

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

Theorem: !rflagsbits->pf$inline-of-bfix-pf

(defthm !rflagsbits->pf$inline-of-bfix-pf
  (equal (!rflagsbits->pf$inline (bfix pf) x)
         (!rflagsbits->pf$inline pf x)))

Theorem: !rflagsbits->pf$inline-bit-equiv-congruence-on-pf

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

Theorem: !rflagsbits->pf$inline-of-rflagsbits-fix-x

(defthm !rflagsbits->pf$inline-of-rflagsbits-fix-x
  (equal (!rflagsbits->pf$inline pf (rflagsbits-fix x))
         (!rflagsbits->pf$inline pf x)))

Theorem: !rflagsbits->pf$inline-rflagsbits-equiv-congruence-on-x

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

Theorem: !rflagsbits->pf-is-rflagsbits

(defthm !rflagsbits->pf-is-rflagsbits
  (equal (!rflagsbits->pf pf x)
         (change-rflagsbits x :pf pf)))

Theorem: rflagsbits->pf-of-!rflagsbits->pf

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

Theorem: !rflagsbits->pf-equiv-under-mask

(defthm !rflagsbits->pf-equiv-under-mask
  (b* ((?new-x (!rflagsbits->pf$inline pf x)))
    (rflagsbits-equiv-under-mask new-x x -5)))