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• Abstract-syntax-rename-fn

Struct-declon-list-rename-fn

Signature

(struct-declon-list-rename-fn c$::struct-declon-list uid new-fn) 
  → 
fty::result

Arguments

c$::struct-declon-list — Guard (struct-declon-listp c$::struct-declon-list).

uid — Guard (c$::uidp uid).

new-fn — Guard (identp new-fn).

Returns

fty::result — Type (struct-declon-listp fty::result).

Definitions and Theorems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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