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Grammar

Cst-letter-conc?

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

Definitions and Theorems

Function: cst-letter-conc?

(defun cst-letter-conc? (abnf::cst)
 (declare (xargs :guard (abnf::treep abnf::cst)))
 (declare (xargs :guard (cst-matchp abnf::cst "letter")))
 (let ((__function__ 'cst-letter-conc?))
  (declare (ignorable __function__))
  (cond
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "uppercase-letter"))
     1)
    ((equal
          (abnf::tree-nonleaf->rulename?
               (nth 0
                    (nth 0
                         (abnf::tree-nonleaf->branches abnf::cst))))
          (abnf::rulename "lowercase-letter"))
     2)
    (t (prog2$ (impossible) 1)))))

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

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

Theorem: cst-letter-conc?-possibilities

(defthm cst-letter-conc?-possibilities
  (b* ((number (cst-letter-conc? abnf::cst)))
    (or (equal number 1) (equal number 2)))
  :rule-classes
  ((:forward-chaining
        :trigger-terms ((cst-letter-conc? abnf::cst)))))

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

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

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

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

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

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

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

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