Function:
(defun smtp-cst-obs-dtext-conc? (cst) (declare (xargs :guard (treep cst))) (declare (xargs :guard (smtp-cst-matchp cst "obs-dtext"))) (let ((__function__ 'smtp-cst-obs-dtext-conc?)) (declare (ignorable __function__)) (cond ((equal (tree-nonleaf->rulename? (nth 0 (nth 0 (tree-nonleaf->branches cst)))) (rulename "obs-no-ws-ctl")) 1) ((equal (tree-nonleaf->rulename? (nth 0 (nth 0 (tree-nonleaf->branches cst)))) (rulename "quoted-pair")) 2) (t (prog2$ (acl2::impossible) 1)))))
Theorem:
(defthm posp-of-smtp-cst-obs-dtext-conc? (b* ((number (smtp-cst-obs-dtext-conc? cst))) (posp number)) :rule-classes :rewrite)
Theorem:
(defthm smtp-cst-obs-dtext-conc?-possibilities (b* ((number (smtp-cst-obs-dtext-conc? cst))) (or (equal number 1) (equal number 2))) :rule-classes ((:forward-chaining :trigger-terms ((smtp-cst-obs-dtext-conc? cst)))))
Theorem:
(defthm smtp-cst-obs-dtext-conc?-of-tree-fix-cst (equal (smtp-cst-obs-dtext-conc? (tree-fix cst)) (smtp-cst-obs-dtext-conc? cst)))
Theorem:
(defthm smtp-cst-obs-dtext-conc?-tree-equiv-congruence-on-cst (implies (tree-equiv cst cst-equiv) (equal (smtp-cst-obs-dtext-conc? cst) (smtp-cst-obs-dtext-conc? cst-equiv))) :rule-classes :congruence)
Theorem:
(defthm smtp-cst-obs-dtext-conc?-1-iff-match-conc (implies (smtp-cst-matchp cst "obs-dtext") (iff (equal (smtp-cst-obs-dtext-conc? cst) 1) (smtp-cst-list-list-conc-matchp (tree-nonleaf->branches cst) "obs-no-ws-ctl"))))
Theorem:
(defthm smtp-cst-obs-dtext-conc?-2-iff-match-conc (implies (smtp-cst-matchp cst "obs-dtext") (iff (equal (smtp-cst-obs-dtext-conc? cst) 2) (smtp-cst-list-list-conc-matchp (tree-nonleaf->branches cst) "quoted-pair"))))