Function:
(defun imap-cst-command-auth-conc10-rep-elem (cst) (declare (xargs :guard (treep cst))) (declare (xargs :guard (and (imap-cst-matchp cst "command-auth") (equal (imap-cst-command-auth-conc? cst) 10)))) (let ((__function__ 'imap-cst-command-auth-conc10-rep-elem)) (declare (ignorable __function__)) (tree-fix (nth 0 (imap-cst-command-auth-conc10-rep cst)))))
Theorem:
(defthm treep-of-imap-cst-command-auth-conc10-rep-elem (b* ((cst1 (imap-cst-command-auth-conc10-rep-elem cst))) (treep cst1)) :rule-classes :rewrite)
Theorem:
(defthm imap-cst-command-auth-conc10-rep-elem-match (implies (and (imap-cst-matchp cst "command-auth") (equal (imap-cst-command-auth-conc? cst) 10)) (b* ((cst1 (imap-cst-command-auth-conc10-rep-elem cst))) (imap-cst-matchp cst1 "subscribe"))) :rule-classes :rewrite)
Theorem:
(defthm imap-cst-command-auth-conc10-rep-elem-of-tree-fix-cst (equal (imap-cst-command-auth-conc10-rep-elem (tree-fix cst)) (imap-cst-command-auth-conc10-rep-elem cst)))
Theorem:
(defthm imap-cst-command-auth-conc10-rep-elem-tree-equiv-congruence-on-cst (implies (tree-equiv cst cst-equiv) (equal (imap-cst-command-auth-conc10-rep-elem cst) (imap-cst-command-auth-conc10-rep-elem cst-equiv))) :rule-classes :congruence)