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• Fgl-function-mode

!fgl-function-mode->dont-rewrite

Update the |FGL|::|DONT-REWRITE| field of a fgl-function-mode bit structure.

Signature

(!fgl-function-mode->dont-rewrite dont-rewrite x) → new-x

Arguments

dont-rewrite — Guard (booleanp dont-rewrite).

x — Guard (fgl-function-mode-p x).

Returns

new-x — Type (fgl-function-mode-p new-x).

Definitions and Theorems

Function: !fgl-function-mode->dont-rewrite

(defun !fgl-function-mode->dont-rewrite (dont-rewrite x)
  (declare (xargs :guard (and (booleanp dont-rewrite)
                              (fgl-function-mode-p x))))
  (mbe :logic
       (b* ((dont-rewrite (bool->bit dont-rewrite))
            (x (fgl-function-mode-fix x)))
         (acl2::part-install dont-rewrite x
                             :width 1
                             :low 3))
       :exec (the (unsigned-byte 6)
                  (logior (the (unsigned-byte 6)
                               (logand (the (unsigned-byte 6) x)
                                       (the (signed-byte 5) -9)))
                          (the (unsigned-byte 4)
                               (ash (the (unsigned-byte 1)
                                         (bool->bit dont-rewrite))
                                    3))))))

Theorem: fgl-function-mode-p-of-!fgl-function-mode->dont-rewrite

(defthm fgl-function-mode-p-of-!fgl-function-mode->dont-rewrite
  (b* ((new-x (!fgl-function-mode->dont-rewrite dont-rewrite x)))
    (fgl-function-mode-p new-x))
  :rule-classes :rewrite)

Theorem: !fgl-function-mode->dont-rewrite-of-bool-fix-dont-rewrite

(defthm !fgl-function-mode->dont-rewrite-of-bool-fix-dont-rewrite
  (equal (!fgl-function-mode->dont-rewrite (bool-fix dont-rewrite)
                                           x)
         (!fgl-function-mode->dont-rewrite dont-rewrite x)))

Theorem: !fgl-function-mode->dont-rewrite-iff-congruence-on-dont-rewrite

(defthm
    !fgl-function-mode->dont-rewrite-iff-congruence-on-dont-rewrite
 (implies
    (iff dont-rewrite dont-rewrite-equiv)
    (equal (!fgl-function-mode->dont-rewrite dont-rewrite x)
           (!fgl-function-mode->dont-rewrite dont-rewrite-equiv x)))
 :rule-classes :congruence)

Theorem: !fgl-function-mode->dont-rewrite-of-fgl-function-mode-fix-x

(defthm !fgl-function-mode->dont-rewrite-of-fgl-function-mode-fix-x
  (equal (!fgl-function-mode->dont-rewrite
              dont-rewrite (fgl-function-mode-fix x))
         (!fgl-function-mode->dont-rewrite dont-rewrite x)))

Theorem: !fgl-function-mode->dont-rewrite-fgl-function-mode-equiv-congruence-on-x

(defthm
 !fgl-function-mode->dont-rewrite-fgl-function-mode-equiv-congruence-on-x
 (implies
    (fgl-function-mode-equiv x x-equiv)
    (equal (!fgl-function-mode->dont-rewrite dont-rewrite x)
           (!fgl-function-mode->dont-rewrite dont-rewrite x-equiv)))
 :rule-classes :congruence)

Theorem: !fgl-function-mode->dont-rewrite-is-fgl-function-mode

(defthm !fgl-function-mode->dont-rewrite-is-fgl-function-mode
  (equal (!fgl-function-mode->dont-rewrite dont-rewrite x)
         (change-fgl-function-mode x
                                   :dont-rewrite dont-rewrite)))

Theorem: fgl-function-mode->dont-rewrite-of-!fgl-function-mode->dont-rewrite

(defthm
 fgl-function-mode->dont-rewrite-of-!fgl-function-mode->dont-rewrite
 (b* ((?new-x (!fgl-function-mode->dont-rewrite dont-rewrite x)))
   (equal (fgl-function-mode->dont-rewrite new-x)
          (bool-fix dont-rewrite))))

Theorem: !fgl-function-mode->dont-rewrite-equiv-under-mask

(defthm !fgl-function-mode->dont-rewrite-equiv-under-mask
  (b* ((?new-x (!fgl-function-mode->dont-rewrite dont-rewrite x)))
    (fgl-function-mode-equiv-under-mask new-x x -9)))