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• Abstract-syntax-replace-field-access

Spec/qual-list-replace-field-access

Signature

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

Arguments

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

Definitions and Theorems

Theorem: spec/qual-list-replace-field-access-type-prescription

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

Theorem: spec/qual-list-replace-field-access-when-atom

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

Theorem: spec/qual-list-replace-field-access-of-cons

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

Theorem: spec/qual-list-replace-field-access-of-append

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

Theorem: consp-of-spec/qual-list-replace-field-access

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

Theorem: len-of-spec/qual-list-replace-field-access

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

Theorem: nth-of-spec/qual-list-replace-field-access

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

Theorem: spec/qual-list-replace-field-access-of-revappend

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

Theorem: spec/qual-list-replace-field-access-of-reverse

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