Function:
(defun uri-cst-host-conc2-rep-elem (cst) (declare (xargs :guard (treep cst))) (declare (xargs :guard (and (uri-cst-matchp cst "host") (equal (uri-cst-host-conc? cst) 2)))) (let ((__function__ 'uri-cst-host-conc2-rep-elem)) (declare (ignorable __function__)) (tree-fix (nth 0 (uri-cst-host-conc2-rep cst)))))
Theorem:
(defthm treep-of-uri-cst-host-conc2-rep-elem (b* ((cst1 (uri-cst-host-conc2-rep-elem cst))) (treep cst1)) :rule-classes :rewrite)
Theorem:
(defthm uri-cst-host-conc2-rep-elem-match (implies (and (uri-cst-matchp cst "host") (equal (uri-cst-host-conc? cst) 2)) (b* ((cst1 (uri-cst-host-conc2-rep-elem cst))) (uri-cst-matchp cst1 "ipv4address"))) :rule-classes :rewrite)
Theorem:
(defthm uri-cst-host-conc2-rep-elem-of-tree-fix-cst (equal (uri-cst-host-conc2-rep-elem (tree-fix cst)) (uri-cst-host-conc2-rep-elem cst)))
Theorem:
(defthm uri-cst-host-conc2-rep-elem-tree-equiv-congruence-on-cst (implies (tree-equiv cst cst-equiv) (equal (uri-cst-host-conc2-rep-elem cst) (uri-cst-host-conc2-rep-elem cst-equiv))) :rule-classes :congruence)