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Cutinfo

!cutinfo->valid

Update the |AIGNET|::|VALID| field of a cutinfo bit structure.

Signature
(!cutinfo->valid valid x) → new-x
Arguments: valid — Guard (booleanp valid).; x — Guard (cutinfo-p x).
Returns: new-x — Type (cutinfo-p new-x).

Definitions and Theorems

Function: !cutinfo->valid

(defun !cutinfo->valid (valid x)
 (declare (xargs :guard (and (booleanp valid) (cutinfo-p x))))
 (mbe
    :logic
    (b* ((valid (bool->bit valid))
         (x (cutinfo-fix x)))
      (part-install valid x :width 1 :low 19))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 21) -524289)))
                       (the (unsigned-byte 20)
                            (ash (the (unsigned-byte 1)
                                      (bool->bit valid))
                                 19))))))

Theorem: cutinfo-p-of-!cutinfo->valid

(defthm cutinfo-p-of-!cutinfo->valid
  (b* ((new-x (!cutinfo->valid valid x)))
    (cutinfo-p new-x))
  :rule-classes :rewrite)

Theorem: !cutinfo->valid-of-bool-fix-valid

(defthm !cutinfo->valid-of-bool-fix-valid
  (equal (!cutinfo->valid (acl2::bool-fix valid)
                          x)
         (!cutinfo->valid valid x)))

Theorem: !cutinfo->valid-iff-congruence-on-valid

(defthm !cutinfo->valid-iff-congruence-on-valid
  (implies (iff valid valid-equiv)
           (equal (!cutinfo->valid valid x)
                  (!cutinfo->valid valid-equiv x)))
  :rule-classes :congruence)

Theorem: !cutinfo->valid-of-cutinfo-fix-x

(defthm !cutinfo->valid-of-cutinfo-fix-x
  (equal (!cutinfo->valid valid (cutinfo-fix x))
         (!cutinfo->valid valid x)))

Theorem: !cutinfo->valid-cutinfo-equiv-congruence-on-x

(defthm !cutinfo->valid-cutinfo-equiv-congruence-on-x
  (implies (cutinfo-equiv x x-equiv)
           (equal (!cutinfo->valid valid x)
                  (!cutinfo->valid valid x-equiv)))
  :rule-classes :congruence)

Theorem: !cutinfo->valid-is-cutinfo

(defthm !cutinfo->valid-is-cutinfo
  (equal (!cutinfo->valid valid x)
         (change-cutinfo x :valid valid)))

Theorem: cutinfo->valid-of-!cutinfo->valid

(defthm cutinfo->valid-of-!cutinfo->valid
  (b* ((?new-x (!cutinfo->valid valid x)))
    (equal (cutinfo->valid new-x)
           (acl2::bool-fix valid))))

Theorem: !cutinfo->valid-equiv-under-mask

(defthm !cutinfo->valid-equiv-under-mask
  (b* ((?new-x (!cutinfo->valid valid x)))
    (cutinfo-equiv-under-mask new-x x -524289)))