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    • Renaming-variables

    Add-vars-to-var-renaming

    Add the variables in a list to a variable renaming list.

    Signature
    (add-vars-to-var-renaming old new ren) → new-ren
    Arguments
    old — Guard (identifier-listp old).
    new — Guard (identifier-listp new).
    ren — Guard (renamingp ren).
    Returns
    new-ren — Type (renaming-resultp new-ren).

    Definitions and Theorems

    Function: add-vars-to-var-renaming

    (defun add-vars-to-var-renaming (old new ren)
     (declare (xargs :guard (and (identifier-listp old)
                                 (identifier-listp new)
                                 (renamingp ren))))
     (let ((__function__ 'add-vars-to-var-renaming))
      (declare (ignorable __function__))
      (b*
       (((when (endp old))
         (if (endp new)
             (renaming-fix ren)
           (reserrf
                (list :mismatch-extra-new (identifier-list-fix new)))))
        ((when (endp new))
         (reserrf (list :mismatch-extra-old (identifier-list-fix old))))
        ((okf ren)
         (add-var-to-var-renaming (car old)
                                  (car new)
                                  ren)))
       (add-vars-to-var-renaming (cdr old)
                                 (cdr new)
                                 ren))))

    Theorem: renaming-resultp-of-add-vars-to-var-renaming

    (defthm renaming-resultp-of-add-vars-to-var-renaming
      (b* ((new-ren (add-vars-to-var-renaming old new ren)))
        (renaming-resultp new-ren))
      :rule-classes :rewrite)

    Theorem: same-len-when-add-vars-to-var-renaming

    (defthm same-len-when-add-vars-to-var-renaming
      (implies (not (reserrp (add-vars-to-var-renaming old new ren)))
               (equal (len new) (len old))))

    Theorem: subsetp-equal-of-add-vars-to-var-renaming

    (defthm subsetp-equal-of-add-vars-to-var-renaming
      (b* ((ren1 (add-vars-to-var-renaming old new ren)))
        (implies (not (reserrp ren1))
                 (subsetp-equal (renaming->list ren)
                                (renaming->list ren1)))))

    Theorem: var-renamevar-of-add-vars-to-var-renaming-when-var-renamevar

    (defthm var-renamevar-of-add-vars-to-var-renaming-when-var-renamevar
      (b* ((ren1 (add-vars-to-var-renaming old1 new1 ren)))
        (implies (and (not (reserrp ren1))
                      (not (reserrp (var-renamevar old new ren))))
                 (not (reserrp (var-renamevar old new ren1))))))

    Theorem: var-list-renamevar-when-add-vars-to-var-renaming

    (defthm var-list-renamevar-when-add-vars-to-var-renaming
      (b* ((ren1 (add-vars-to-var-renaming old new ren)))
        (implies (not (reserrp ren1))
                 (not (reserrp (var-list-renamevar old new ren1))))))

    Theorem: add-vars-to-var-renaming-of-identifier-list-fix-old

    (defthm add-vars-to-var-renaming-of-identifier-list-fix-old
      (equal (add-vars-to-var-renaming (identifier-list-fix old)
                                       new ren)
             (add-vars-to-var-renaming old new ren)))

    Theorem: add-vars-to-var-renaming-identifier-list-equiv-congruence-on-old

    (defthm
       add-vars-to-var-renaming-identifier-list-equiv-congruence-on-old
      (implies (identifier-list-equiv old old-equiv)
               (equal (add-vars-to-var-renaming old new ren)
                      (add-vars-to-var-renaming old-equiv new ren)))
      :rule-classes :congruence)

    Theorem: add-vars-to-var-renaming-of-identifier-list-fix-new

    (defthm add-vars-to-var-renaming-of-identifier-list-fix-new
      (equal (add-vars-to-var-renaming old (identifier-list-fix new)
                                       ren)
             (add-vars-to-var-renaming old new ren)))

    Theorem: add-vars-to-var-renaming-identifier-list-equiv-congruence-on-new

    (defthm
       add-vars-to-var-renaming-identifier-list-equiv-congruence-on-new
      (implies (identifier-list-equiv new new-equiv)
               (equal (add-vars-to-var-renaming old new ren)
                      (add-vars-to-var-renaming old new-equiv ren)))
      :rule-classes :congruence)

    Theorem: add-vars-to-var-renaming-of-renaming-fix-ren

    (defthm add-vars-to-var-renaming-of-renaming-fix-ren
      (equal (add-vars-to-var-renaming old new (renaming-fix ren))
             (add-vars-to-var-renaming old new ren)))

    Theorem: add-vars-to-var-renaming-renaming-equiv-congruence-on-ren

    (defthm add-vars-to-var-renaming-renaming-equiv-congruence-on-ren
      (implies (renaming-equiv ren ren-equiv)
               (equal (add-vars-to-var-renaming old new ren)
                      (add-vars-to-var-renaming old new ren-equiv)))
      :rule-classes :congruence)