		Search-engine friendly clone of the ACL2 documentation.

Grammar

Cst-command-conc?

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

Definitions and Theorems

Function: cst-command-conc?

(defun cst-command-conc? (abnf::cst)
 (declare (xargs :guard (abnf::treep abnf::cst)))
 (declare (xargs :guard (cst-matchp abnf::cst "command")))
 (let ((__function__ 'cst-command-conc?))
  (declare (ignorable __function__))
  (cond
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "contains"))
     1)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "get"))
     2)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "get-or-use"))
     3)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "set"))
     4)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "remove"))
     5)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "random"))
     6)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "position"))
     7)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "branch"))
     8)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "await"))
     9)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "instruction"))
     10)
    (t (prog2$ (impossible) 1)))))

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

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

Theorem: cst-command-conc?-possibilities

(defthm cst-command-conc?-possibilities
  (b* ((number (cst-command-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)
        (equal number 8)
        (equal number 9)
        (equal number 10)))
  :rule-classes
  ((:forward-chaining
        :trigger-terms ((cst-command-conc? abnf::cst)))))

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

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

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

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

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

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

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

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

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

(defthm cst-command-conc?-3-iff-match-conc
  (implies (cst-matchp abnf::cst "command")
           (iff (equal (cst-command-conc? abnf::cst) 3)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "get-or-use"))))

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

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

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

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

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

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

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

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

Theorem: cst-command-conc?-8-iff-match-conc

(defthm cst-command-conc?-8-iff-match-conc
  (implies (cst-matchp abnf::cst "command")
           (iff (equal (cst-command-conc? abnf::cst) 8)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "branch"))))

Theorem: cst-command-conc?-9-iff-match-conc

(defthm cst-command-conc?-9-iff-match-conc
  (implies (cst-matchp abnf::cst "command")
           (iff (equal (cst-command-conc? abnf::cst) 9)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "await"))))

Theorem: cst-command-conc?-10-iff-match-conc

(defthm cst-command-conc?-10-iff-match-conc
  (implies (cst-matchp abnf::cst "command")
           (iff (equal (cst-command-conc? abnf::cst) 10)
                (cst-list-list-conc-matchp
                     (abnf::tree-nonleaf->branches abnf::cst)
                     "instruction"))))