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• Abstract-syntax-rename

Struct-declon-list-rename

Signature

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

Arguments

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

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

Returns

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

Definitions and Theorems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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