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Abstract-syntax-rename-fn

Desiniter-list-rename-fn

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

Definitions and Theorems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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