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• Abstract-syntax-rename

Extdecl-list-rename

Signature

(extdecl-list-rename c$::extdecl-list subst) → fty::result

Arguments

c$::extdecl-list — Guard (extdecl-listp c$::extdecl-list).

subst — Guard (ident-ident-alistp subst).

Returns

fty::result — Type (extdecl-listp fty::result).

Definitions and Theorems

Function: extdecl-list-rename

(defun extdecl-list-rename (c$::extdecl-list subst)
  (declare (xargs :guard (and (extdecl-listp c$::extdecl-list)
                              (ident-ident-alistp subst))))
  (let ((__function__ 'extdecl-list-rename))
    (declare (ignorable __function__))
    (if (endp c$::extdecl-list)
        nil
      (cons (extdecl-rename (car c$::extdecl-list)
                            subst)
            (extdecl-list-rename (cdr c$::extdecl-list)
                                 subst)))))

Theorem: extdecl-listp-of-extdecl-list-rename

(defthm extdecl-listp-of-extdecl-list-rename
  (b* ((fty::result (extdecl-list-rename c$::extdecl-list subst)))
    (extdecl-listp fty::result))
  :rule-classes :rewrite)

Theorem: extdecl-list-rename-type-prescription

(defthm extdecl-list-rename-type-prescription
  (true-listp (extdecl-list-rename c$::extdecl-list subst))
  :rule-classes :type-prescription)

Theorem: extdecl-list-rename-when-atom

(defthm extdecl-list-rename-when-atom
  (implies (atom c$::extdecl-list)
           (equal (extdecl-list-rename c$::extdecl-list subst)
                  nil)))

Theorem: extdecl-list-rename-of-cons

(defthm extdecl-list-rename-of-cons
  (equal (extdecl-list-rename (cons c$::extdecl c$::extdecl-list)
                              subst)
         (cons (extdecl-rename c$::extdecl subst)
               (extdecl-list-rename c$::extdecl-list subst))))

Theorem: extdecl-list-rename-of-append

(defthm extdecl-list-rename-of-append
  (equal (extdecl-list-rename (append acl2::x acl2::y)
                              subst)
         (append (extdecl-list-rename acl2::x subst)
                 (extdecl-list-rename acl2::y subst))))

Theorem: consp-of-extdecl-list-rename

(defthm consp-of-extdecl-list-rename
  (equal (consp (extdecl-list-rename c$::extdecl-list subst))
         (consp c$::extdecl-list)))

Theorem: len-of-extdecl-list-rename

(defthm len-of-extdecl-list-rename
  (equal (len (extdecl-list-rename c$::extdecl-list subst))
         (len c$::extdecl-list)))

Theorem: nth-of-extdecl-list-rename

(defthm nth-of-extdecl-list-rename
  (equal (nth acl2::n
              (extdecl-list-rename c$::extdecl-list subst))
         (if (< (nfix acl2::n)
                (len c$::extdecl-list))
             (extdecl-rename (nth acl2::n c$::extdecl-list)
                             subst)
           nil)))

Theorem: extdecl-list-rename-of-revappend

(defthm extdecl-list-rename-of-revappend
  (equal (extdecl-list-rename (revappend acl2::x acl2::y)
                              subst)
         (revappend (extdecl-list-rename acl2::x subst)
                    (extdecl-list-rename acl2::y subst))))

Theorem: extdecl-list-rename-of-reverse

(defthm extdecl-list-rename-of-reverse
  (equal (extdecl-list-rename (reverse c$::extdecl-list)
                              subst)
         (reverse (extdecl-list-rename c$::extdecl-list subst))))

Theorem: extdecl-list-rename-of-extdecl-list-fix-extdecl-list

(defthm extdecl-list-rename-of-extdecl-list-fix-extdecl-list
  (equal (extdecl-list-rename (extdecl-list-fix c$::extdecl-list)
                              subst)
         (extdecl-list-rename c$::extdecl-list subst)))

Theorem: extdecl-list-rename-extdecl-list-equiv-congruence-on-extdecl-list

(defthm
  extdecl-list-rename-extdecl-list-equiv-congruence-on-extdecl-list
  (implies
       (c$::extdecl-list-equiv c$::extdecl-list extdecl-list-equiv)
       (equal (extdecl-list-rename c$::extdecl-list subst)
              (extdecl-list-rename extdecl-list-equiv subst)))
  :rule-classes :congruence)

Theorem: extdecl-list-rename-of-ident-ident-alist-fix-subst

(defthm extdecl-list-rename-of-ident-ident-alist-fix-subst
  (equal (extdecl-list-rename c$::extdecl-list
                              (ident-ident-alist-fix subst))
         (extdecl-list-rename c$::extdecl-list subst)))

Theorem: extdecl-list-rename-ident-ident-alist-equiv-congruence-on-subst

(defthm
    extdecl-list-rename-ident-ident-alist-equiv-congruence-on-subst
  (implies
       (ident-ident-alist-equiv subst subst-equiv)
       (equal (extdecl-list-rename c$::extdecl-list subst)
              (extdecl-list-rename c$::extdecl-list subst-equiv)))
  :rule-classes :congruence)