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• Abstract-syntax-rename

Block-item-list-rename

Signature

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

Arguments

c$::block-item-list — Guard (block-item-listp c$::block-item-list).

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

Returns

fty::result — Type (block-item-listp fty::result).

Definitions and Theorems

Theorem: block-item-list-rename-type-prescription

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

Theorem: block-item-list-rename-when-atom

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

Theorem: block-item-list-rename-of-cons

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

Theorem: block-item-list-rename-of-append

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

Theorem: consp-of-block-item-list-rename

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

Theorem: len-of-block-item-list-rename

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

Theorem: nth-of-block-item-list-rename

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

Theorem: block-item-list-rename-of-revappend

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

Theorem: block-item-list-rename-of-reverse

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