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Abstract-syntax-rename-fn

Init-declor-list-rename-fn

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

Definitions and Theorems

Theorem: init-declor-list-rename-fn-type-prescription

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

Theorem: init-declor-list-rename-fn-when-atom

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

Theorem: init-declor-list-rename-fn-of-cons

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

Theorem: init-declor-list-rename-fn-of-append

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

Theorem: consp-of-init-declor-list-rename-fn

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

Theorem: len-of-init-declor-list-rename-fn

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

Theorem: nth-of-init-declor-list-rename-fn

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

Theorem: init-declor-list-rename-fn-of-revappend

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

Theorem: init-declor-list-rename-fn-of-reverse

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