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• Abstract-syntax-replace-field-access

Struct-declon-list-replace-field-access

Signature

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

Arguments

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

Definitions and Theorems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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