		Search-engine friendly clone of the ACL2 documentation.

Grammar

Cst-value-conc?

Signature
(cst-value-conc? abnf::cst) → number
Arguments: abnf::cst — Guard (abnf::treep abnf::cst).
Returns: number — Type (posp number).

Definitions and Theorems

Function: cst-value-conc?

(defun cst-value-conc? (abnf::cst)
 (declare (xargs :guard (abnf::treep abnf::cst)))
 (declare (xargs :guard (cst-matchp abnf::cst "value")))
 (let ((__function__ 'cst-value-conc?))
  (declare (ignorable __function__))
  (cond
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "false"))
     1)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "null"))
     2)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "true"))
     3)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "object"))
     4)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "array"))
     5)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "number"))
     6)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "string"))
     7)
    (t (prog2$ (acl2::impossible) 1)))))

Theorem: posp-of-cst-value-conc?

(defthm posp-of-cst-value-conc?
  (b* ((number (cst-value-conc? abnf::cst)))
    (posp number))
  :rule-classes :rewrite)

Theorem: cst-value-conc?-possibilities

(defthm cst-value-conc?-possibilities
 (b* ((number (cst-value-conc? abnf::cst)))
   (or (equal number 1)
       (equal number 2)
       (equal number 3)
       (equal number 4)
       (equal number 5)
       (equal number 6)
       (equal number 7)))
 :rule-classes
 ((:forward-chaining :trigger-terms ((cst-value-conc? abnf::cst)))))

Theorem: cst-value-conc?-of-tree-fix-cst

(defthm cst-value-conc?-of-tree-fix-cst
  (equal (cst-value-conc? (abnf::tree-fix abnf::cst))
         (cst-value-conc? abnf::cst)))

Theorem: cst-value-conc?-tree-equiv-congruence-on-cst

(defthm cst-value-conc?-tree-equiv-congruence-on-cst
  (implies (abnf::tree-equiv abnf::cst cst-equiv)
           (equal (cst-value-conc? abnf::cst)
                  (cst-value-conc? cst-equiv)))
  :rule-classes :congruence)

Theorem: cst-value-conc?-1-iff-match-conc

(defthm cst-value-conc?-1-iff-match-conc
  (implies (cst-matchp abnf::cst "value")
           (iff (equal (cst-value-conc? abnf::cst) 1)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "false"))))

Theorem: cst-value-conc?-2-iff-match-conc

(defthm cst-value-conc?-2-iff-match-conc
  (implies (cst-matchp abnf::cst "value")
           (iff (equal (cst-value-conc? abnf::cst) 2)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "null"))))

Theorem: cst-value-conc?-3-iff-match-conc

(defthm cst-value-conc?-3-iff-match-conc
  (implies (cst-matchp abnf::cst "value")
           (iff (equal (cst-value-conc? abnf::cst) 3)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "true"))))

Theorem: cst-value-conc?-4-iff-match-conc

(defthm cst-value-conc?-4-iff-match-conc
  (implies (cst-matchp abnf::cst "value")
           (iff (equal (cst-value-conc? abnf::cst) 4)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "object"))))

Theorem: cst-value-conc?-5-iff-match-conc

(defthm cst-value-conc?-5-iff-match-conc
  (implies (cst-matchp abnf::cst "value")
           (iff (equal (cst-value-conc? abnf::cst) 5)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "array"))))

Theorem: cst-value-conc?-6-iff-match-conc

(defthm cst-value-conc?-6-iff-match-conc
  (implies (cst-matchp abnf::cst "value")
           (iff (equal (cst-value-conc? abnf::cst) 6)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "number"))))

Theorem: cst-value-conc?-7-iff-match-conc

(defthm cst-value-conc?-7-iff-match-conc
  (implies (cst-matchp abnf::cst "value")
           (iff (equal (cst-value-conc? abnf::cst) 7)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "string"))))