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Imap-example

Imap-cst-addr-name-conc-rep

Signature
(imap-cst-addr-name-conc-rep cst) → csts
Arguments: cst — Guard (treep cst).
Returns: csts — Type (tree-listp csts).

Definitions and Theorems

Function: imap-cst-addr-name-conc-rep

(defun imap-cst-addr-name-conc-rep (cst)
  (declare (xargs :guard (treep cst)))
  (declare (xargs :guard (imap-cst-matchp cst "addr-name")))
  (let ((__function__ 'imap-cst-addr-name-conc-rep))
    (declare (ignorable __function__))
    (tree-list-fix (nth 0 (imap-cst-addr-name-conc cst)))))

Theorem: tree-listp-of-imap-cst-addr-name-conc-rep

(defthm tree-listp-of-imap-cst-addr-name-conc-rep
  (b* ((csts (imap-cst-addr-name-conc-rep cst)))
    (tree-listp csts))
  :rule-classes :rewrite)

Theorem: imap-cst-addr-name-conc-rep-match

(defthm imap-cst-addr-name-conc-rep-match
  (implies (imap-cst-matchp cst "addr-name")
           (b* ((csts (imap-cst-addr-name-conc-rep cst)))
             (imap-cst-list-rep-matchp csts "nstring")))
  :rule-classes :rewrite)

Theorem: imap-cst-addr-name-conc-rep-of-tree-fix-cst

(defthm imap-cst-addr-name-conc-rep-of-tree-fix-cst
  (equal (imap-cst-addr-name-conc-rep (tree-fix cst))
         (imap-cst-addr-name-conc-rep cst)))

Theorem: imap-cst-addr-name-conc-rep-tree-equiv-congruence-on-cst

(defthm imap-cst-addr-name-conc-rep-tree-equiv-congruence-on-cst
  (implies (tree-equiv cst cst-equiv)
           (equal (imap-cst-addr-name-conc-rep cst)
                  (imap-cst-addr-name-conc-rep cst-equiv)))
  :rule-classes :congruence)