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              • Vl-read-binary-base-prefix/remainder-thms
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Vl-read-binary-base

binary_base ::= '[s|S]b | '[s|S]B.

Signature

(vl-read-binary-base echars) → (mv prefix remainder)

Arguments

echars — Guard (vl-echarlist-p echars).

Embedded spaces are not allowed.

Definitions and Theorems

Function: vl-read-binary-base$inline

(defun vl-read-binary-base$inline (echars)
  (declare (xargs :guard (vl-echarlist-p echars)))
  (let ((__function__ 'vl-read-binary-base))
    (declare (ignorable __function__))
    (vl-read-some-literal '("'b" "'B" "'sb" "'sB" "'Sb" "'SB")
                          echars)))

Theorem: prefix-of-vl-read-binary-base

(defthm prefix-of-vl-read-binary-base
 (and
     (true-listp (mv-nth 0 (vl-read-binary-base echars)))
     (implies
          (force (vl-echarlist-p echars))
          (vl-echarlist-p (mv-nth 0 (vl-read-binary-base echars)))))
 :rule-classes
 ((:rewrite)
  (:type-prescription
       :corollary
       (true-listp (mv-nth 0 (vl-read-binary-base echars))))))

Theorem: remainder-of-vl-read-binary-base

(defthm remainder-of-vl-read-binary-base
 (and
     (equal (true-listp (mv-nth 1 (vl-read-binary-base echars)))
            (true-listp echars))
     (implies
          (force (vl-echarlist-p echars))
          (vl-echarlist-p (mv-nth 1 (vl-read-binary-base echars)))))
 :rule-classes
 ((:rewrite)
  (:type-prescription
   :corollary
   (implies (true-listp echars)
            (true-listp (mv-nth 1 (vl-read-binary-base echars)))))))

Theorem: append-of-vl-read-binary-base

(defthm append-of-vl-read-binary-base
  (equal (append (mv-nth 0 (vl-read-binary-base echars))
                 (mv-nth 1 (vl-read-binary-base echars)))
         echars))

Theorem: no-change-loser-of-vl-read-binary-base

(defthm no-change-loser-of-vl-read-binary-base
  (implies (not (mv-nth 0 (vl-read-binary-base echars)))
           (equal (mv-nth 1 (vl-read-binary-base echars))
                  echars)))

Theorem: acl2-count-of-vl-read-binary-base-weak

(defthm acl2-count-of-vl-read-binary-base-weak
  (<= (acl2-count (mv-nth 1 (vl-read-binary-base echars)))
      (acl2-count echars))
  :rule-classes ((:rewrite) (:linear)))

Theorem: acl2-count-of-vl-read-binary-base-strong

(defthm acl2-count-of-vl-read-binary-base-strong
  (implies (mv-nth 0 (vl-read-binary-base echars))
           (< (acl2-count (mv-nth 1 (vl-read-binary-base echars)))
              (acl2-count echars)))
  :rule-classes ((:rewrite) (:linear)))

Subtopics

Vl-read-binary-base-prefix/remainder-thms

Prefix and remainder theorems for vl-read-binary-base, automatically generated by def-prefix/remainder-thms.