Function:
(defun smtp-cst-sp-conc-rep-elem (cst) (declare (xargs :guard (treep cst))) (declare (xargs :guard (smtp-cst-matchp cst "sp"))) (let ((__function__ 'smtp-cst-sp-conc-rep-elem)) (declare (ignorable __function__)) (tree-fix (nth 0 (smtp-cst-sp-conc-rep cst)))))
Theorem:
(defthm treep-of-smtp-cst-sp-conc-rep-elem (b* ((cst1 (smtp-cst-sp-conc-rep-elem cst))) (treep cst1)) :rule-classes :rewrite)
Theorem:
(defthm smtp-cst-sp-conc-rep-elem-match (implies (smtp-cst-matchp cst "sp") (b* ((cst1 (smtp-cst-sp-conc-rep-elem cst))) (smtp-cst-matchp cst1 "%x20"))) :rule-classes :rewrite)
Theorem:
(defthm smtp-cst-sp-conc-rep-elem-of-tree-fix-cst (equal (smtp-cst-sp-conc-rep-elem (tree-fix cst)) (smtp-cst-sp-conc-rep-elem cst)))
Theorem:
(defthm smtp-cst-sp-conc-rep-elem-tree-equiv-congruence-on-cst (implies (tree-equiv cst cst-equiv) (equal (smtp-cst-sp-conc-rep-elem cst) (smtp-cst-sp-conc-rep-elem cst-equiv))) :rule-classes :congruence)