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• Abstract-syntax-rename-fn

Spec/qual-list-rename-fn

Signature

(spec/qual-list-rename-fn c$::spec/qual-list uid new-fn) 
  → 
fty::result

Arguments

c$::spec/qual-list — Guard (spec/qual-listp c$::spec/qual-list).

uid — Guard (c$::uidp uid).

new-fn — Guard (identp new-fn).

Returns

fty::result — Type (spec/qual-listp fty::result).

Definitions and Theorems

Theorem: spec/qual-list-rename-fn-type-prescription

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

Theorem: spec/qual-list-rename-fn-when-atom

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

Theorem: spec/qual-list-rename-fn-of-cons

(defthm spec/qual-list-rename-fn-of-cons
 (equal
   (spec/qual-list-rename-fn (cons c$::spec/qual c$::spec/qual-list)
                             uid new-fn)
   (cons (spec/qual-rename-fn c$::spec/qual uid new-fn)
         (spec/qual-list-rename-fn c$::spec/qual-list uid new-fn))))

Theorem: spec/qual-list-rename-fn-of-append

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

Theorem: consp-of-spec/qual-list-rename-fn

(defthm consp-of-spec/qual-list-rename-fn
 (equal
    (consp (spec/qual-list-rename-fn c$::spec/qual-list uid new-fn))
    (consp c$::spec/qual-list)))

Theorem: len-of-spec/qual-list-rename-fn

(defthm len-of-spec/qual-list-rename-fn
 (equal
      (len (spec/qual-list-rename-fn c$::spec/qual-list uid new-fn))
      (len c$::spec/qual-list)))

Theorem: nth-of-spec/qual-list-rename-fn

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

Theorem: spec/qual-list-rename-fn-of-revappend

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

Theorem: spec/qual-list-rename-fn-of-reverse

(defthm spec/qual-list-rename-fn-of-reverse
 (equal
    (spec/qual-list-rename-fn (reverse c$::spec/qual-list)
                              uid new-fn)
    (reverse
         (spec/qual-list-rename-fn c$::spec/qual-list uid new-fn))))