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• Vl-lex-token1
• Def-token/remainder-thms

Vl-lex-token1-token/remainder-thms

Token and remainder theorems for vl-lex-token1, automatically generated by def-token/remainder-thms.

Definitions and Theorems

Theorem: vl-token-p-of-vl-lex-token1

(defthm vl-token-p-of-vl-lex-token1
 (implies
  (and (force (vl-echarlist-p echars))
       (and (force (consp echars))
            (force (equal char1 (vl-echar->char (car echars))))
            (force (booleanp breakp))
            (force (vl-lexstate-p st))))
  (equal
      (vl-token-p
           (mv-nth 0
                   (vl-lex-token1 char1 echars breakp st warnings)))
      (if (mv-nth 0
                  (vl-lex-token1 char1 echars breakp st warnings))
          t
        nil))))

Theorem: true-listp-of-vl-lex-token1

(defthm true-listp-of-vl-lex-token1
 (equal
      (true-listp
           (mv-nth 1
                   (vl-lex-token1 char1 echars breakp st warnings)))
      (true-listp echars))
 :rule-classes
 ((:rewrite)
  (:type-prescription
   :corollary
   (implies
    (true-listp echars)
    (true-listp
       (mv-nth 1
               (vl-lex-token1 char1 echars breakp st warnings)))))))

Theorem: vl-echarlist-p-of-vl-lex-token1

(defthm vl-echarlist-p-of-vl-lex-token1
 (implies
  (force (vl-echarlist-p echars))
  (equal
      (vl-echarlist-p
           (mv-nth 1
                   (vl-lex-token1 char1 echars breakp st warnings)))
      t)))

Theorem: append-of-vl-lex-token1

(defthm append-of-vl-lex-token1
 (implies
  (and (mv-nth 0
               (vl-lex-token1 char1 echars breakp st warnings))
       (force (vl-echarlist-p echars))
       (and (force (consp echars))
            (force (equal char1 (vl-echar->char (car echars))))
            (force (booleanp breakp))
            (force (vl-lexstate-p st))))
  (equal
   (append
      (vl-token->etext
           (mv-nth 0
                   (vl-lex-token1 char1 echars breakp st warnings)))
      (mv-nth 1
              (vl-lex-token1 char1 echars breakp st warnings)))
   echars)))

Theorem: no-change-loser-of-vl-lex-token1

(defthm no-change-loser-of-vl-lex-token1
 (implies
     (not (mv-nth 0
                  (vl-lex-token1 char1 echars breakp st warnings)))
     (equal (mv-nth 1
                    (vl-lex-token1 char1 echars breakp st warnings))
            echars)))

Theorem: acl2-count-of-vl-lex-token1-weak

(defthm acl2-count-of-vl-lex-token1-weak
  (<= (acl2-count
           (mv-nth 1
                   (vl-lex-token1 char1 echars breakp st warnings)))
      (acl2-count echars))
  :rule-classes ((:rewrite) (:linear)))

Theorem: acl2-count-of-vl-lex-token1-strong

(defthm acl2-count-of-vl-lex-token1-strong
 (implies
   (and (mv-nth 0
                (vl-lex-token1 char1 echars breakp st warnings))
        (force (equal char1 (vl-echar->char (car echars)))))
   (< (acl2-count
           (mv-nth 1
                   (vl-lex-token1 char1 echars breakp st warnings)))
      (acl2-count echars)))
 :rule-classes ((:rewrite) (:linear)))