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Abstract-syntax-rename-fn

Designor-list-rename-fn

Signature
(designor-list-rename-fn c$::designor-list uid new-fn) → fty::result
Arguments: c$::designor-list — Guard (designor-listp c$::designor-list).; uid — Guard (c$::uidp uid).; new-fn — Guard (identp new-fn).
Returns: fty::result — Type (designor-listp fty::result).

Definitions and Theorems

Theorem: designor-list-rename-fn-type-prescription

(defthm designor-list-rename-fn-type-prescription
 (true-listp (designor-list-rename-fn c$::designor-list uid new-fn))
 :rule-classes :type-prescription)

Theorem: designor-list-rename-fn-when-atom

(defthm designor-list-rename-fn-when-atom
  (implies
       (atom c$::designor-list)
       (equal (designor-list-rename-fn c$::designor-list uid new-fn)
              nil)))

Theorem: designor-list-rename-fn-of-cons

(defthm designor-list-rename-fn-of-cons
 (equal
     (designor-list-rename-fn (cons c$::designor c$::designor-list)
                              uid new-fn)
     (cons (designor-rename-fn c$::designor uid new-fn)
           (designor-list-rename-fn c$::designor-list uid new-fn))))

Theorem: designor-list-rename-fn-of-append

(defthm designor-list-rename-fn-of-append
  (equal (designor-list-rename-fn (append acl2::x acl2::y)
                                  uid new-fn)
         (append (designor-list-rename-fn acl2::x uid new-fn)
                 (designor-list-rename-fn acl2::y uid new-fn))))

Theorem: consp-of-designor-list-rename-fn

(defthm consp-of-designor-list-rename-fn
 (equal
      (consp (designor-list-rename-fn c$::designor-list uid new-fn))
      (consp c$::designor-list)))

Theorem: len-of-designor-list-rename-fn

(defthm len-of-designor-list-rename-fn
 (equal (len (designor-list-rename-fn c$::designor-list uid new-fn))
        (len c$::designor-list)))

Theorem: nth-of-designor-list-rename-fn

(defthm nth-of-designor-list-rename-fn
 (equal (nth acl2::n
             (designor-list-rename-fn c$::designor-list uid new-fn))
        (if (< (nfix acl2::n)
               (len c$::designor-list))
            (designor-rename-fn (nth acl2::n c$::designor-list)
                                uid new-fn)
          nil)))

Theorem: designor-list-rename-fn-of-revappend

(defthm designor-list-rename-fn-of-revappend
  (equal (designor-list-rename-fn (revappend acl2::x acl2::y)
                                  uid new-fn)
         (revappend (designor-list-rename-fn acl2::x uid new-fn)
                    (designor-list-rename-fn acl2::y uid new-fn))))

Theorem: designor-list-rename-fn-of-reverse

(defthm designor-list-rename-fn-of-reverse
 (equal
  (designor-list-rename-fn (reverse c$::designor-list)
                           uid new-fn)
  (reverse (designor-list-rename-fn c$::designor-list uid new-fn))))