(http-cst-uri-host-conc3-rep cst) → csts
Function:
(defun http-cst-uri-host-conc3-rep (cst) (declare (xargs :guard (treep cst))) (declare (xargs :guard (and (http-cst-matchp cst "uri-host") (equal (http-cst-uri-host-conc? cst) 3)))) (let ((__function__ 'http-cst-uri-host-conc3-rep)) (declare (ignorable __function__)) (tree-list-fix (nth 0 (http-cst-uri-host-conc3 cst)))))
Theorem:
(defthm tree-listp-of-http-cst-uri-host-conc3-rep (b* ((csts (http-cst-uri-host-conc3-rep cst))) (tree-listp csts)) :rule-classes :rewrite)
Theorem:
(defthm http-cst-uri-host-conc3-rep-match (implies (and (http-cst-matchp cst "uri-host") (equal (http-cst-uri-host-conc? cst) 3)) (b* ((csts (http-cst-uri-host-conc3-rep cst))) (http-cst-list-rep-matchp csts "reg-name"))) :rule-classes :rewrite)
Theorem:
(defthm http-cst-uri-host-conc3-rep-of-tree-fix-cst (equal (http-cst-uri-host-conc3-rep (tree-fix cst)) (http-cst-uri-host-conc3-rep cst)))
Theorem:
(defthm http-cst-uri-host-conc3-rep-tree-equiv-congruence-on-cst (implies (tree-equiv cst cst-equiv) (equal (http-cst-uri-host-conc3-rep cst) (http-cst-uri-host-conc3-rep cst-equiv))) :rule-classes :congruence)