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• Abstract-syntax-replace-field-access

Filepath-transunit-map-replace-field-access

Signature

(filepath-transunit-map-replace-field-access 
     c$::filepath-transunit-map original 
     linkage new1 new2 split-members) 
 
  → 
fty::result

Arguments

c$::filepath-transunit-map — Guard (filepath-transunit-mapp c$::filepath-transunit-map).

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 (filepath-transunit-mapp fty::result).

Definitions and Theorems

Function: filepath-transunit-map-replace-field-access

(defun filepath-transunit-map-replace-field-access
       (c$::filepath-transunit-map original
                                   linkage new1 new2 split-members)
 (declare
  (xargs
    :guard (and (filepath-transunit-mapp c$::filepath-transunit-map)
                (identp original)
                (c$::linkagep linkage)
                (identp new1)
                (identp new2)
                (ident-listp split-members))))
 (let ((__function__ 'filepath-transunit-map-replace-field-access))
  (declare (ignorable __function__))
  (if
   (or
    (not (mbt (filepath-transunit-mapp c$::filepath-transunit-map)))
    (omap::emptyp c$::filepath-transunit-map))
   nil
   (omap::update (omap::head-key c$::filepath-transunit-map)
                 (transunit-replace-field-access
                      (omap::head-val c$::filepath-transunit-map)
                      original
                      linkage new1 new2 split-members)
                 (filepath-transunit-map-replace-field-access
                      (omap::tail c$::filepath-transunit-map)
                      original
                      linkage new1 new2 split-members)))))

Theorem: filepath-transunit-mapp-of-filepath-transunit-map-replace-field-access

(defthm
 filepath-transunit-mapp-of-filepath-transunit-map-replace-field-access
 (b* ((fty::result (filepath-transunit-map-replace-field-access
                        c$::filepath-transunit-map original
                        linkage new1 new2 split-members)))
   (filepath-transunit-mapp fty::result))
 :rule-classes :rewrite)

Theorem: filepath-transunit-map-replace-field-access-type-prescription

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

Theorem: filepath-transunit-map-replace-field-access-when-emptyp

(defthm filepath-transunit-map-replace-field-access-when-emptyp
  (implies (omap::emptyp c$::filepath-transunit-map)
           (equal (filepath-transunit-map-replace-field-access
                       c$::filepath-transunit-map original
                       linkage new1 new2 split-members)
                  nil)))

Theorem: emptyp-of-filepath-transunit-map-replace-field-access

(defthm emptyp-of-filepath-transunit-map-replace-field-access
 (equal
  (omap::emptyp (filepath-transunit-map-replace-field-access
                     c$::filepath-transunit-map original
                     linkage new1 new2 split-members))
  (omap::emptyp
      (c$::filepath-transunit-map-fix c$::filepath-transunit-map))))

Theorem: keys-of-filepath-transunit-map-replace-field-access

(defthm keys-of-filepath-transunit-map-replace-field-access
 (equal
  (omap::keys (filepath-transunit-map-replace-field-access
                   c$::filepath-transunit-map original
                   linkage new1 new2 split-members))
  (omap::keys
      (c$::filepath-transunit-map-fix c$::filepath-transunit-map))))

Theorem: assoc-of-filepath-transunit-map-replace-field-access

(defthm assoc-of-filepath-transunit-map-replace-field-access
 (equal
  (omap::assoc fty::key
               (filepath-transunit-map-replace-field-access
                    c$::filepath-transunit-map original
                    linkage new1 new2 split-members))
  (if
   (omap::assoc
        fty::key
        (c$::filepath-transunit-map-fix c$::filepath-transunit-map))
   (cons
    fty::key
    (transunit-replace-field-access
     (cdr
      (omap::assoc
       fty::key
       (c$::filepath-transunit-map-fix c$::filepath-transunit-map)))
     original
     linkage new1 new2 split-members))
   nil)))

Theorem: filepath-transunit-map-replace-field-access-of-filepath-transunit-map-fix-filepath-transunit-map

(defthm
 filepath-transunit-map-replace-field-access-of-filepath-transunit-map-fix-filepath-transunit-map
 (equal
    (filepath-transunit-map-replace-field-access
         (c$::filepath-transunit-map-fix c$::filepath-transunit-map)
         original
         linkage new1 new2 split-members)
    (filepath-transunit-map-replace-field-access
         c$::filepath-transunit-map original
         linkage new1 new2 split-members)))

Theorem: filepath-transunit-map-replace-field-access-filepath-transunit-map-equiv-congruence-on-filepath-transunit-map

(defthm
 filepath-transunit-map-replace-field-access-filepath-transunit-map-equiv-congruence-on-filepath-transunit-map
 (implies
     (c$::filepath-transunit-map-equiv c$::filepath-transunit-map
                                       filepath-transunit-map-equiv)
     (equal (filepath-transunit-map-replace-field-access
                 c$::filepath-transunit-map original
                 linkage new1 new2 split-members)
            (filepath-transunit-map-replace-field-access
                 filepath-transunit-map-equiv original
                 linkage new1 new2 split-members)))
 :rule-classes :congruence)

Theorem: filepath-transunit-map-replace-field-access-of-ident-fix-original

(defthm
  filepath-transunit-map-replace-field-access-of-ident-fix-original
  (equal (filepath-transunit-map-replace-field-access
              c$::filepath-transunit-map
              (ident-fix original)
              linkage new1 new2 split-members)
         (filepath-transunit-map-replace-field-access
              c$::filepath-transunit-map original
              linkage new1 new2 split-members)))

Theorem: filepath-transunit-map-replace-field-access-ident-equiv-congruence-on-original

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

Theorem: filepath-transunit-map-replace-field-access-of-linkage-fix-linkage

(defthm
 filepath-transunit-map-replace-field-access-of-linkage-fix-linkage
 (equal (filepath-transunit-map-replace-field-access
             c$::filepath-transunit-map
             original (c$::linkage-fix linkage)
             new1 new2 split-members)
        (filepath-transunit-map-replace-field-access
             c$::filepath-transunit-map original
             linkage new1 new2 split-members)))

Theorem: filepath-transunit-map-replace-field-access-linkage-equiv-congruence-on-linkage

(defthm
 filepath-transunit-map-replace-field-access-linkage-equiv-congruence-on-linkage
 (implies (c$::linkage-equiv linkage linkage-equiv)
          (equal (filepath-transunit-map-replace-field-access
                      c$::filepath-transunit-map original
                      linkage new1 new2 split-members)
                 (filepath-transunit-map-replace-field-access
                      c$::filepath-transunit-map original
                      linkage-equiv new1 new2 split-members)))
 :rule-classes :congruence)

Theorem: filepath-transunit-map-replace-field-access-of-ident-fix-new1

(defthm
      filepath-transunit-map-replace-field-access-of-ident-fix-new1
  (equal (filepath-transunit-map-replace-field-access
              c$::filepath-transunit-map
              original linkage (ident-fix new1)
              new2 split-members)
         (filepath-transunit-map-replace-field-access
              c$::filepath-transunit-map original
              linkage new1 new2 split-members)))

Theorem: filepath-transunit-map-replace-field-access-ident-equiv-congruence-on-new1

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

Theorem: filepath-transunit-map-replace-field-access-of-ident-fix-new2

(defthm
      filepath-transunit-map-replace-field-access-of-ident-fix-new2
  (equal (filepath-transunit-map-replace-field-access
              c$::filepath-transunit-map
              original linkage new1 (ident-fix new2)
              split-members)
         (filepath-transunit-map-replace-field-access
              c$::filepath-transunit-map original
              linkage new1 new2 split-members)))

Theorem: filepath-transunit-map-replace-field-access-ident-equiv-congruence-on-new2

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

Theorem: filepath-transunit-map-replace-field-access-of-ident-list-fix-split-members

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

Theorem: filepath-transunit-map-replace-field-access-ident-list-equiv-congruence-on-split-members

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