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Renaming

Renaming->list

Get the list field from a renaming.

Signature
(renaming->list x) → list
Arguments: x — Guard (renamingp x).
Returns: list — Type (identifier-identifier-alistp list).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: renaming->list$inline

(defun renaming->list$inline (x)
 (declare (xargs :guard (renamingp x)))
 (declare (xargs :guard t))
 (let ((__function__ 'renaming->list))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((x (and t x))
     (list
         (identifier-identifier-alist-fix (cdr (std::da-nth 0 x)))))
    (if (and (no-duplicatesp-equal (strip-cars list))
             (no-duplicatesp-equal (strip-cdrs list)))
        list
      nil))
   :exec (cdr (std::da-nth 0 x)))))

Theorem: identifier-identifier-alistp-of-renaming->list

(defthm identifier-identifier-alistp-of-renaming->list
  (b* ((list (renaming->list$inline x)))
    (identifier-identifier-alistp list))
  :rule-classes :rewrite)

Theorem: renaming->list$inline-of-renaming-fix-x

(defthm renaming->list$inline-of-renaming-fix-x
  (equal (renaming->list$inline (renaming-fix x))
         (renaming->list$inline x)))

Theorem: renaming->list$inline-renaming-equiv-congruence-on-x

(defthm renaming->list$inline-renaming-equiv-congruence-on-x
  (implies (renaming-equiv x x-equiv)
           (equal (renaming->list$inline x)
                  (renaming->list$inline x-equiv)))
  :rule-classes :congruence)