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• Major-stack-p

Major-stack-p-basics

Basic theorems about major-stack-p, generated by deflist.

Definitions and Theorems

Theorem: major-stack-p-of-cons

(defthm major-stack-p-of-cons
  (implies (major-stack-p x)
           (iff (major-stack-p (cons a x))
                (major-frame-p a)))
  :rule-classes ((:rewrite)))

Theorem: major-stack-p-of-singleton

(defthm major-stack-p-of-singleton
  (iff (major-stack-p (cons a nil))
       (major-frame-p a))
  :rule-classes ((:rewrite)))

Theorem: major-stack-p-of-cdr-when-major-stack-p

(defthm major-stack-p-of-cdr-when-major-stack-p
  (implies (and (major-stack-p (double-rewrite x))
                (consp (cdr x)))
           (major-stack-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: major-stack-p-when-not-consp

(defthm major-stack-p-when-not-consp
  (implies (not (consp x))
           (not (major-stack-p x)))
  :rule-classes ((:rewrite)))

Theorem: major-stack-p-implies-consp

(defthm major-stack-p-implies-consp
  (implies (major-stack-p x) (consp x))
  :rule-classes
  ((:forward-chaining
        :trigger-terms ((acl2::element-list-nonempty-p x)))))

Theorem: major-frame-p-of-car-when-major-stack-p

(defthm major-frame-p-of-car-when-major-stack-p
  (implies (major-stack-p x)
           (major-frame-p (car x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-major-stack-p

(defthm true-listp-when-major-stack-p
  (implies (major-stack-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: major-stack-p-of-append

(defthm major-stack-p-of-append
  (implies (and (major-stack-p a)
                (major-stack-p b))
           (major-stack-p (append a b)))
  :rule-classes ((:rewrite)))