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• Abstract-syntax-replace-field-access

Genassoc-list-replace-field-access

Signature

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

Arguments

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

Definitions and Theorems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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