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• Abstract-syntax-replace-field-access

Ext-declon-list-replace-field-access

Signature

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

Arguments

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

Definitions and Theorems

Function: ext-declon-list-replace-field-access

(defun ext-declon-list-replace-field-access
       (c$::ext-declon-list original
                            linkage new1 new2 split-members)
  (declare (xargs :guard (and (ext-declon-listp c$::ext-declon-list)
                              (identp original)
                              (c$::linkagep linkage)
                              (identp new1)
                              (identp new2)
                              (ident-listp split-members))))
  (let ((__function__ 'ext-declon-list-replace-field-access))
    (declare (ignorable __function__))
    (if (endp c$::ext-declon-list)
        nil
      (cons (ext-declon-replace-field-access
                 (car c$::ext-declon-list)
                 original
                 linkage new1 new2 split-members)
            (ext-declon-list-replace-field-access
                 (cdr c$::ext-declon-list)
                 original
                 linkage new1 new2 split-members)))))

Theorem: ext-declon-listp-of-ext-declon-list-replace-field-access

(defthm ext-declon-listp-of-ext-declon-list-replace-field-access
  (b* ((fty::result (ext-declon-list-replace-field-access
                         c$::ext-declon-list original
                         linkage new1 new2 split-members)))
    (ext-declon-listp fty::result))
  :rule-classes :rewrite)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: ext-declon-list-replace-field-access-of-ext-declon-list-fix-ext-declon-list

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

Theorem: ext-declon-list-replace-field-access-ext-declon-list-equiv-congruence-on-ext-declon-list

(defthm
 ext-declon-list-replace-field-access-ext-declon-list-equiv-congruence-on-ext-declon-list
 (implies (c$::ext-declon-list-equiv c$::ext-declon-list
                                     ext-declon-list-equiv)
          (equal (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage new1 new2 split-members)
                 (ext-declon-list-replace-field-access
                      ext-declon-list-equiv original
                      linkage new1 new2 split-members)))
 :rule-classes :congruence)

Theorem: ext-declon-list-replace-field-access-of-ident-fix-original

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

Theorem: ext-declon-list-replace-field-access-ident-equiv-congruence-on-original

(defthm
 ext-declon-list-replace-field-access-ident-equiv-congruence-on-original
 (implies (c$::ident-equiv original original-equiv)
          (equal (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage new1 new2 split-members)
                 (ext-declon-list-replace-field-access
                      c$::ext-declon-list original-equiv
                      linkage new1 new2 split-members)))
 :rule-classes :congruence)

Theorem: ext-declon-list-replace-field-access-of-linkage-fix-linkage

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

Theorem: ext-declon-list-replace-field-access-linkage-equiv-congruence-on-linkage

(defthm
 ext-declon-list-replace-field-access-linkage-equiv-congruence-on-linkage
 (implies (c$::linkage-equiv linkage linkage-equiv)
          (equal (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage new1 new2 split-members)
                 (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage-equiv new1 new2 split-members)))
 :rule-classes :congruence)

Theorem: ext-declon-list-replace-field-access-of-ident-fix-new1

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

Theorem: ext-declon-list-replace-field-access-ident-equiv-congruence-on-new1

(defthm
 ext-declon-list-replace-field-access-ident-equiv-congruence-on-new1
 (implies (c$::ident-equiv new1 new1-equiv)
          (equal (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage new1 new2 split-members)
                 (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage new1-equiv new2 split-members)))
 :rule-classes :congruence)

Theorem: ext-declon-list-replace-field-access-of-ident-fix-new2

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

Theorem: ext-declon-list-replace-field-access-ident-equiv-congruence-on-new2

(defthm
 ext-declon-list-replace-field-access-ident-equiv-congruence-on-new2
 (implies (c$::ident-equiv new2 new2-equiv)
          (equal (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage new1 new2 split-members)
                 (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage new1 new2-equiv split-members)))
 :rule-classes :congruence)

Theorem: ext-declon-list-replace-field-access-of-ident-list-fix-split-members

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

Theorem: ext-declon-list-replace-field-access-ident-list-equiv-congruence-on-split-members

(defthm
 ext-declon-list-replace-field-access-ident-list-equiv-congruence-on-split-members
 (implies (c$::ident-list-equiv split-members split-members-equiv)
          (equal (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage new1 new2 split-members)
                 (ext-declon-list-replace-field-access
                      c$::ext-declon-list original
                      linkage new1 new2 split-members-equiv)))
 :rule-classes :congruence)