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

hex_base ::= '[s|S]h | '[s|S]H.

Signature

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

Arguments

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

Embedded spaces are not allowed.

Definitions and Theorems

Function: vl-read-hex-base$inline

(defun vl-read-hex-base$inline (echars)
  (declare (xargs :guard (vl-echarlist-p echars)))
  (let ((__function__ 'vl-read-hex-base))
    (declare (ignorable __function__))
    (vl-read-some-literal '("'h" "'H" "'sh" "'sH" "'Sh" "'SH")
                          echars)))

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

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

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

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

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

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

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

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

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

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

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

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

Subtopics

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

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