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Rational-listp

Rational-listp-basics

Basic theorems about rational-listp, generated by std::deflist.

Definitions and Theorems

Theorem: rational-listp-of-cons

(defthm rational-listp-of-cons
        (equal (rational-listp (cons a x))
               (and (rationalp a) (rational-listp x)))
        :rule-classes ((:rewrite)))

Theorem: rational-listp-of-cdr-when-rational-listp

(defthm rational-listp-of-cdr-when-rational-listp
        (implies (rational-listp (double-rewrite x))
                 (rational-listp (cdr x)))
        :rule-classes ((:rewrite)))

Theorem: rational-listp-when-not-consp

(defthm rational-listp-when-not-consp
        (implies (not (consp x))
                 (equal (rational-listp x) (not x)))
        :rule-classes ((:rewrite)))

Theorem: rationalp-of-car-when-rational-listp

(defthm rationalp-of-car-when-rational-listp
        (implies (rational-listp x)
                 (iff (rationalp (car x)) (consp x)))
        :rule-classes ((:rewrite)))

Theorem: true-listp-when-rational-listp-compound-recognizer

(defthm true-listp-when-rational-listp-compound-recognizer
        (implies (rational-listp x)
                 (true-listp x))
        :rule-classes :compound-recognizer)

Theorem: rational-listp-of-list-fix

(defthm rational-listp-of-list-fix
        (implies (rational-listp x)
                 (rational-listp (list-fix x)))
        :rule-classes ((:rewrite)))

Theorem: rational-listp-of-rev

(defthm rational-listp-of-rev
        (equal (rational-listp (rev x))
               (rational-listp (list-fix x)))
        :rule-classes ((:rewrite)))