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Smtp-example

Smtp-cst-local-part-conc2-rep

Signature
(smtp-cst-local-part-conc2-rep cst) → csts
Arguments: cst — Guard (treep cst).
Returns: csts — Type (tree-listp csts).

Definitions and Theorems

Function: smtp-cst-local-part-conc2-rep

(defun smtp-cst-local-part-conc2-rep (cst)
  (declare (xargs :guard (treep cst)))
  (declare (xargs :guard (and (smtp-cst-matchp cst "local-part")
                              (equal (smtp-cst-local-part-conc? cst)
                                     2))))
  (let ((__function__ 'smtp-cst-local-part-conc2-rep))
    (declare (ignorable __function__))
    (tree-list-fix (nth 0 (smtp-cst-local-part-conc2 cst)))))

Theorem: tree-listp-of-smtp-cst-local-part-conc2-rep

(defthm tree-listp-of-smtp-cst-local-part-conc2-rep
  (b* ((csts (smtp-cst-local-part-conc2-rep cst)))
    (tree-listp csts))
  :rule-classes :rewrite)

Theorem: smtp-cst-local-part-conc2-rep-match

(defthm smtp-cst-local-part-conc2-rep-match
  (implies (and (smtp-cst-matchp cst "local-part")
                (equal (smtp-cst-local-part-conc? cst)
                       2))
           (b* ((csts (smtp-cst-local-part-conc2-rep cst)))
             (smtp-cst-list-rep-matchp csts "quoted-string")))
  :rule-classes :rewrite)

Theorem: smtp-cst-local-part-conc2-rep-of-tree-fix-cst

(defthm smtp-cst-local-part-conc2-rep-of-tree-fix-cst
  (equal (smtp-cst-local-part-conc2-rep (tree-fix cst))
         (smtp-cst-local-part-conc2-rep cst)))

Theorem: smtp-cst-local-part-conc2-rep-tree-equiv-congruence-on-cst

(defthm smtp-cst-local-part-conc2-rep-tree-equiv-congruence-on-cst
  (implies (tree-equiv cst cst-equiv)
           (equal (smtp-cst-local-part-conc2-rep cst)
                  (smtp-cst-local-part-conc2-rep cst-equiv)))
  :rule-classes :congruence)