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G-integer

G-integer->bits

Get the bits field from a g-integer.

Signature
(g-integer->bits x) → bits
Arguments: x — Guard (fgl-object-p x).
Returns: bits — Type (true-listp bits).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: g-integer->bits$inline

(defun g-integer->bits$inline (x)
  (declare (xargs :guard (fgl-object-p x)))
  (declare (xargs :guard (equal (fgl-object-kind x) :g-integer)))
  (let ((__function__ 'g-integer->bits))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (fgl-object-kind x) :g-integer)
                      x)))
           (list-fix (cdr x)))
         :exec (cdr x))))

Theorem: true-listp-of-g-integer->bits

(defthm true-listp-of-g-integer->bits
  (b* ((bits (g-integer->bits$inline x)))
    (true-listp bits))
  :rule-classes :rewrite)

Theorem: g-integer->bits$inline-of-fgl-object-fix-x

(defthm g-integer->bits$inline-of-fgl-object-fix-x
  (equal (g-integer->bits$inline (fgl-object-fix x))
         (g-integer->bits$inline x)))

Theorem: g-integer->bits$inline-fgl-object-equiv-congruence-on-x

(defthm g-integer->bits$inline-fgl-object-equiv-congruence-on-x
  (implies (fgl-object-equiv x x-equiv)
           (equal (g-integer->bits$inline x)
                  (g-integer->bits$inline x-equiv)))
  :rule-classes :congruence)

Theorem: g-integer->bits-when-wrong-kind

(defthm g-integer->bits-when-wrong-kind
  (implies (not (equal (fgl-object-kind x) :g-integer))
           (equal (g-integer->bits x)
                  (list-fix nil))))