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• Std/lists/abstract

Elementlist-projection

Generic projection over a typed list.

Definitions and Theorems

Function: elementlist-projection

(defun elementlist-projection (x)
       (if (atom x)
           nil
           (cons (element-xformer (car x))
                 (elementlist-projection (cdr x)))))

Theorem: outelement-list-p-of-elementlist-projection

(defthm outelement-list-p-of-elementlist-projection
        (implies (element-list-p x)
                 (outelement-list-p (elementlist-projection x)))
        :rule-classes :rewrite)

Theorem: elementlist-projection-of-cons

(defthm elementlist-projection-of-cons
        (equal (elementlist-projection (cons a b))
               (cons (element-xformer a)
                     (elementlist-projection b)))
        :rule-classes :rewrite)

Theorem: elementlist-projection-when-not-consp

(defthm elementlist-projection-when-not-consp
        (implies (not (consp x))
                 (equal (elementlist-projection x) nil))
        :rule-classes :rewrite)

Theorem: true-listp-of-elementlist-projection

(defthm true-listp-of-elementlist-projection
        (true-listp (elementlist-projection x))
        :rule-classes :type-prescription)

Theorem: len-of-elementlist-projection

(defthm len-of-elementlist-projection
        (equal (len (elementlist-projection x))
               (len x))
        :rule-classes :rewrite)

Theorem: consp-of-elementlist-projection

(defthm consp-of-elementlist-projection
        (equal (consp (elementlist-projection x))
               (consp x))
        :rule-classes :rewrite)

Theorem: elementlist-projection-under-iff

(defthm elementlist-projection-under-iff
        (iff (elementlist-projection x)
             (consp x))
        :rule-classes :rewrite)

Theorem: car-of-elementlist-projection-when-nil-preservingp

(defthm car-of-elementlist-projection-when-nil-preservingp
        (implies (equal nil (element-xformer nil))
                 (equal (car (elementlist-projection x))
                        (element-xformer (car x))))
        :rule-classes :rewrite)

Theorem: car-of-elementlist-projection

(defthm car-of-elementlist-projection
        (equal (car (elementlist-projection x))
               (and (consp x)
                    (element-xformer (car x))))
        :rule-classes :rewrite)

Theorem: cdr-of-elementlist-projection

(defthm cdr-of-elementlist-projection
        (equal (cdr (elementlist-projection x))
               (elementlist-projection (cdr x)))
        :rule-classes :rewrite)

Theorem: elementlist-projection-of-append

(defthm elementlist-projection-of-append
        (equal (elementlist-projection (append a b))
               (append (elementlist-projection a)
                       (elementlist-projection b)))
        :rule-classes :rewrite)