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• Atc-var-info-listp

Atc-var-info-listp-basics

Basic theorems about atc-var-info-listp, generated by std::deflist.

Definitions and Theorems

Theorem: atc-var-info-listp-of-cons

(defthm atc-var-info-listp-of-cons
  (equal (atc-var-info-listp (cons acl2::a acl2::x))
         (and (atc-var-infop acl2::a)
              (atc-var-info-listp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: atc-var-info-listp-of-cdr-when-atc-var-info-listp

(defthm atc-var-info-listp-of-cdr-when-atc-var-info-listp
  (implies (atc-var-info-listp (double-rewrite acl2::x))
           (atc-var-info-listp (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: atc-var-info-listp-when-not-consp

(defthm atc-var-info-listp-when-not-consp
  (implies (not (consp acl2::x))
           (equal (atc-var-info-listp acl2::x)
                  (not acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: atc-var-infop-of-car-when-atc-var-info-listp

(defthm atc-var-infop-of-car-when-atc-var-info-listp
  (implies (atc-var-info-listp acl2::x)
           (iff (atc-var-infop (car acl2::x))
                (consp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-atc-var-info-listp-compound-recognizer

(defthm true-listp-when-atc-var-info-listp-compound-recognizer
  (implies (atc-var-info-listp acl2::x)
           (true-listp acl2::x))
  :rule-classes :compound-recognizer)

Theorem: atc-var-info-listp-of-list-fix

(defthm atc-var-info-listp-of-list-fix
  (implies (atc-var-info-listp acl2::x)
           (atc-var-info-listp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: atc-var-info-listp-of-rev

(defthm atc-var-info-listp-of-rev
  (equal (atc-var-info-listp (rev acl2::x))
         (atc-var-info-listp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: atc-var-info-listp-of-append

(defthm atc-var-info-listp-of-append
  (equal (atc-var-info-listp (append acl2::a acl2::b))
         (and (atc-var-info-listp (list-fix acl2::a))
              (atc-var-info-listp acl2::b)))
  :rule-classes ((:rewrite)))