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• Abstract-syntax-rename

Ext-declon-list-rename

Signature

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

Arguments

c$::ext-declon-list — Guard (ext-declon-listp c$::ext-declon-list).

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

Returns

fty::result — Type (ext-declon-listp fty::result).

Definitions and Theorems

Function: ext-declon-list-rename

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

Theorem: ext-declon-listp-of-ext-declon-list-rename

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

Theorem: ext-declon-list-rename-type-prescription

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

Theorem: ext-declon-list-rename-when-atom

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

Theorem: ext-declon-list-rename-of-cons

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

Theorem: ext-declon-list-rename-of-append

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

Theorem: consp-of-ext-declon-list-rename

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

Theorem: len-of-ext-declon-list-rename

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

Theorem: nth-of-ext-declon-list-rename

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

Theorem: ext-declon-list-rename-of-revappend

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

Theorem: ext-declon-list-rename-of-reverse

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

Theorem: ext-declon-list-rename-of-ext-declon-list-fix-ext-declon-list

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

Theorem: ext-declon-list-rename-ext-declon-list-equiv-congruence-on-ext-declon-list

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

Theorem: ext-declon-list-rename-of-ident-ident-alist-fix-subst

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

Theorem: ext-declon-list-rename-ident-ident-alist-equiv-congruence-on-subst

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