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Bexp

Bexp-count

Measure for recurring over bexp structures.

Signature
(bexp-count x) → count
Arguments: x — Guard (bexpp x).
Returns: count — Type (natp count).

Definitions and Theorems

Function: bexp-count

(defun bexp-count (x)
  (declare (xargs :guard (bexpp x)))
  (let ((__function__ 'bexp-count))
    (declare (ignorable __function__))
    (case (bexp-kind x)
      (:const 1)
      (:equal 1)
      (:less 1)
      (:not (+ 2 (bexp-count (bexp-not->arg x))))
      (:and (+ 3 (bexp-count (bexp-and->left x))
               (bexp-count (bexp-and->right x)))))))

Theorem: natp-of-bexp-count

(defthm natp-of-bexp-count
  (b* ((count (bexp-count x)))
    (natp count))
  :rule-classes :type-prescription)

Theorem: bexp-count-of-bexp-fix-x

(defthm bexp-count-of-bexp-fix-x
  (equal (bexp-count (bexp-fix x))
         (bexp-count x)))

Theorem: bexp-count-bexp-equiv-congruence-on-x

(defthm bexp-count-bexp-equiv-congruence-on-x
  (implies (bexp-equiv x x-equiv)
           (equal (bexp-count x)
                  (bexp-count x-equiv)))
  :rule-classes :congruence)

Theorem: bexp-count-of-bexp-not

(defthm bexp-count-of-bexp-not
  (implies t
           (< (+ (bexp-count arg))
              (bexp-count (bexp-not arg))))
  :rule-classes :linear)

Theorem: bexp-count-of-bexp-not->arg

(defthm bexp-count-of-bexp-not->arg
  (implies (equal (bexp-kind x) :not)
           (< (bexp-count (bexp-not->arg x))
              (bexp-count x)))
  :rule-classes :linear)

Theorem: bexp-count-of-bexp-and

(defthm bexp-count-of-bexp-and
  (implies t
           (< (+ (bexp-count left) (bexp-count right))
              (bexp-count (bexp-and left right))))
  :rule-classes :linear)

Theorem: bexp-count-of-bexp-and->left

(defthm bexp-count-of-bexp-and->left
  (implies (equal (bexp-kind x) :and)
           (< (bexp-count (bexp-and->left x))
              (bexp-count x)))
  :rule-classes :linear)

Theorem: bexp-count-of-bexp-and->right

(defthm bexp-count-of-bexp-and->right
  (implies (equal (bexp-kind x) :and)
           (< (bexp-count (bexp-and->right x))
              (bexp-count x)))
  :rule-classes :linear)