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• Abstract-syntax-rename

Desiniter-list-rename

Signature

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

Arguments

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

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

Returns

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

Definitions and Theorems

Theorem: desiniter-list-rename-type-prescription

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

Theorem: desiniter-list-rename-when-atom

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

Theorem: desiniter-list-rename-of-cons

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

Theorem: desiniter-list-rename-of-append

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

Theorem: consp-of-desiniter-list-rename

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

Theorem: len-of-desiniter-list-rename

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

Theorem: nth-of-desiniter-list-rename

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

Theorem: desiniter-list-rename-of-revappend

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

Theorem: desiniter-list-rename-of-reverse

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