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Implementation-environments

Sinteger-bit-roles-value-count

Number of value bit roles in a list of roles of signed integer bits.

Signature
(sinteger-bit-roles-value-count roles) → m
Arguments: roles — Guard (sinteger-bit-role-listp roles).
Returns: m — Type (natp m).

If the list of bit roles is well-formed (see sinteger-bit-roles-wfp), this is the number M of value bits [C17:6.2.6.2/2], whose associated exponents go from 0 to M-1.

Definitions and Theorems

Function: sinteger-bit-roles-value-count

(defun sinteger-bit-roles-value-count (roles)
  (declare (xargs :guard (sinteger-bit-role-listp roles)))
  (let ((__function__ 'sinteger-bit-roles-value-count))
    (declare (ignorable __function__))
    (cond ((endp roles) 0)
          ((sinteger-bit-role-case (car roles)
                                   :value)
           (1+ (sinteger-bit-roles-value-count (cdr roles))))
          (t (sinteger-bit-roles-value-count (cdr roles))))))

Theorem: natp-of-sinteger-bit-roles-value-count

(defthm natp-of-sinteger-bit-roles-value-count
  (b* ((m (sinteger-bit-roles-value-count roles)))
    (natp m))
  :rule-classes :rewrite)

Theorem: sinteger-bit-roles-value-count-alt-def

(defthm sinteger-bit-roles-value-count-alt-def
  (equal (sinteger-bit-roles-value-count roles)
         (len (sinteger-bit-roles-exponents roles))))

Theorem: posp-of-sinteger-bit-roles-value-count

(defthm posp-of-sinteger-bit-roles-value-count
  (implies (sinteger-bit-roles-wfp roles)
           (b* ((m (sinteger-bit-roles-value-count roles)))
             (posp m)))
  :rule-classes (:rewrite :type-prescription))

Theorem: sinteger-bit-roles-value-count-of-append

(defthm sinteger-bit-roles-value-count-of-append
  (equal (sinteger-bit-roles-value-count (append roles1 roles2))
         (+ (sinteger-bit-roles-value-count roles1)
            (sinteger-bit-roles-value-count roles2))))

Theorem: sinteger-bit-roles-value-count-of-sinteger-bit-role-list-fix-roles

(defthm
 sinteger-bit-roles-value-count-of-sinteger-bit-role-list-fix-roles
 (equal (sinteger-bit-roles-value-count
             (sinteger-bit-role-list-fix roles))
        (sinteger-bit-roles-value-count roles)))

Theorem: sinteger-bit-roles-value-count-sinteger-bit-role-list-equiv-congruence-on-roles

(defthm
 sinteger-bit-roles-value-count-sinteger-bit-role-list-equiv-congruence-on-roles
 (implies (sinteger-bit-role-list-equiv roles roles-equiv)
          (equal (sinteger-bit-roles-value-count roles)
                 (sinteger-bit-roles-value-count roles-equiv)))
 :rule-classes :congruence)