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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)