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Abstract-syntax-rename-fn

Declon-list-rename-fn

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

Definitions and Theorems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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