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• Abstract-syntax-replace-field-access

Ext-declon-replace-field-access

Signature

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

Arguments

c$::ext-declon — Guard (ext-declonp c$::ext-declon).

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-declonp fty::result).

Definitions and Theorems

Function: ext-declon-replace-field-access

(defun ext-declon-replace-field-access
       (c$::ext-declon original
                       linkage new1 new2 split-members)
 (declare (xargs :guard (and (ext-declonp c$::ext-declon)
                             (identp original)
                             (c$::linkagep linkage)
                             (identp new1)
                             (identp new2)
                             (ident-listp split-members))))
 (declare (ignorable c$::ext-declon original
                     linkage new1 new2 split-members))
 (let ((__function__ 'ext-declon-replace-field-access))
  (declare (ignorable __function__))
  (ext-declon-case
    c$::ext-declon
    :fundef (ext-declon-fundef
                 (fundef-replace-field-access
                      (ext-declon-fundef->fundef c$::ext-declon)
                      original
                      linkage new1 new2 split-members))
    :declon (ext-declon-declon
                 (declon-replace-field-access
                      (c$::ext-declon-declon->declon c$::ext-declon)
                      original
                      linkage new1 new2 split-members))
    :empty (ext-declon-fix c$::ext-declon)
    :asm (c$::ext-declon-asm
              (asm-stmt-replace-field-access
                   (c$::ext-declon-asm->stmt c$::ext-declon)
                   original
                   linkage new1 new2 split-members)))))

Theorem: ext-declonp-of-ext-declon-replace-field-access

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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