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• Abstract-syntax-rename

Init-declor-list-rename

Signature

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

Arguments

c$::init-declor-list — Guard (init-declor-listp c$::init-declor-list).

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

Returns

fty::result — Type (init-declor-listp fty::result).

Definitions and Theorems

Theorem: init-declor-list-rename-type-prescription

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

Theorem: init-declor-list-rename-when-atom

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

Theorem: init-declor-list-rename-of-cons

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

Theorem: init-declor-list-rename-of-append

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

Theorem: consp-of-init-declor-list-rename

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

Theorem: len-of-init-declor-list-rename

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

Theorem: nth-of-init-declor-list-rename

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

Theorem: init-declor-list-rename-of-revappend

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

Theorem: init-declor-list-rename-of-reverse

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