Function:
(defun http-cst-uri-host-conc? (cst) (declare (xargs :guard (treep cst))) (declare (xargs :guard (http-cst-matchp cst "uri-host"))) (let ((__function__ 'http-cst-uri-host-conc?)) (declare (ignorable __function__)) (cond ((equal (tree-nonleaf->rulename? (nth 0 (nth 0 (tree-nonleaf->branches cst)))) (rulename "ip-literal")) 1) ((equal (tree-nonleaf->rulename? (nth 0 (nth 0 (tree-nonleaf->branches cst)))) (rulename "ipv4address")) 2) ((equal (tree-nonleaf->rulename? (nth 0 (nth 0 (tree-nonleaf->branches cst)))) (rulename "reg-name")) 3) (t (prog2$ (acl2::impossible) 1)))))
Theorem:
(defthm posp-of-http-cst-uri-host-conc? (b* ((number (http-cst-uri-host-conc? cst))) (posp number)) :rule-classes :rewrite)
Theorem:
(defthm http-cst-uri-host-conc?-possibilities (b* ((number (http-cst-uri-host-conc? cst))) (or (equal number 1) (equal number 2) (equal number 3))) :rule-classes ((:forward-chaining :trigger-terms ((http-cst-uri-host-conc? cst)))))
Theorem:
(defthm http-cst-uri-host-conc?-of-tree-fix-cst (equal (http-cst-uri-host-conc? (tree-fix cst)) (http-cst-uri-host-conc? cst)))
Theorem:
(defthm http-cst-uri-host-conc?-tree-equiv-congruence-on-cst (implies (tree-equiv cst cst-equiv) (equal (http-cst-uri-host-conc? cst) (http-cst-uri-host-conc? cst-equiv))) :rule-classes :congruence)
Theorem:
(defthm http-cst-uri-host-conc?-1-iff-match-conc (implies (http-cst-matchp cst "uri-host") (iff (equal (http-cst-uri-host-conc? cst) 1) (http-cst-list-list-conc-matchp (tree-nonleaf->branches cst) "ip-literal"))))
Theorem:
(defthm http-cst-uri-host-conc?-2-iff-match-conc (implies (http-cst-matchp cst "uri-host") (iff (equal (http-cst-uri-host-conc? cst) 2) (http-cst-list-list-conc-matchp (tree-nonleaf->branches cst) "ipv4address"))))
Theorem:
(defthm http-cst-uri-host-conc?-3-iff-match-conc (implies (http-cst-matchp cst "uri-host") (iff (equal (http-cst-uri-host-conc? cst) 3) (http-cst-list-list-conc-matchp (tree-nonleaf->branches cst) "reg-name"))))