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• Abstract-syntax-replace-field-access

Declon-list-replace-field-access

Signature

(declon-list-replace-field-access c$::declon-list original 
                                  linkage new1 new2 split-members) 
 
  → 
fty::result

Arguments

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

original — Guard (identp original).

linkage — Guard (c$::linkagep linkage).

new1 — Guard (identp new1).

new2 — Guard (identp new2).

split-members — Guard (ident-listp split-members).

Returns

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

Definitions and Theorems

Theorem: declon-list-replace-field-access-type-prescription

(defthm declon-list-replace-field-access-type-prescription
  (true-listp (declon-list-replace-field-access
                   c$::declon-list original
                   linkage new1 new2 split-members))
  :rule-classes :type-prescription)

Theorem: declon-list-replace-field-access-when-atom

(defthm declon-list-replace-field-access-when-atom
  (implies (atom c$::declon-list)
           (equal (declon-list-replace-field-access
                       c$::declon-list original
                       linkage new1 new2 split-members)
                  nil)))

Theorem: declon-list-replace-field-access-of-cons

(defthm declon-list-replace-field-access-of-cons
 (equal
  (declon-list-replace-field-access (cons declon c$::declon-list)
                                    original
                                    linkage new1 new2 split-members)
  (cons
       (declon-replace-field-access declon original
                                    linkage new1 new2 split-members)
       (declon-list-replace-field-access
            c$::declon-list original
            linkage new1 new2 split-members))))

Theorem: declon-list-replace-field-access-of-append

(defthm declon-list-replace-field-access-of-append
 (equal
  (declon-list-replace-field-access (append acl2::x acl2::y)
                                    original
                                    linkage new1 new2 split-members)
  (append (declon-list-replace-field-access
               acl2::x original
               linkage new1 new2 split-members)
          (declon-list-replace-field-access
               acl2::y original
               linkage new1 new2 split-members))))

Theorem: consp-of-declon-list-replace-field-access

(defthm consp-of-declon-list-replace-field-access
  (equal (consp (declon-list-replace-field-access
                     c$::declon-list original
                     linkage new1 new2 split-members))
         (consp c$::declon-list)))

Theorem: len-of-declon-list-replace-field-access

(defthm len-of-declon-list-replace-field-access
  (equal (len (declon-list-replace-field-access
                   c$::declon-list original
                   linkage new1 new2 split-members))
         (len c$::declon-list)))

Theorem: nth-of-declon-list-replace-field-access

(defthm nth-of-declon-list-replace-field-access
 (equal
   (nth acl2::n
        (declon-list-replace-field-access
             c$::declon-list original
             linkage new1 new2 split-members))
   (if (< (nfix acl2::n) (len c$::declon-list))
       (declon-replace-field-access (nth acl2::n c$::declon-list)
                                    original
                                    linkage new1 new2 split-members)
     nil)))

Theorem: declon-list-replace-field-access-of-revappend

(defthm declon-list-replace-field-access-of-revappend
 (equal
  (declon-list-replace-field-access (revappend acl2::x acl2::y)
                                    original
                                    linkage new1 new2 split-members)
  (revappend (declon-list-replace-field-access
                  acl2::x original
                  linkage new1 new2 split-members)
             (declon-list-replace-field-access
                  acl2::y original
                  linkage new1 new2 split-members))))

Theorem: declon-list-replace-field-access-of-reverse

(defthm declon-list-replace-field-access-of-reverse
 (equal
  (declon-list-replace-field-access (reverse c$::declon-list)
                                    original
                                    linkage new1 new2 split-members)
  (reverse (declon-list-replace-field-access
                c$::declon-list original
                linkage new1 new2 split-members))))