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• Std/lists
• Intersectp

Std/lists/intersectp

Lemmas about intersectp available in the std/lists library.

Definitions and Theorems

Theorem: intersectp-equal-of-atom-left

(defthm intersectp-equal-of-atom-left
        (implies (atom x)
                 (equal (intersectp-equal x y) nil)))

Theorem: intersectp-equal-of-atom-right

(defthm intersectp-equal-of-atom-right
        (implies (atom y)
                 (equal (intersectp-equal x y) nil)))

Theorem: intersect-equal-of-cons-left

(defthm intersect-equal-of-cons-left
        (equal (intersectp-equal (cons a x) y)
               (if (member-equal a y)
                   t (intersectp-equal x y))))

Theorem: intersectp-equal-of-cons-right

(defthm intersectp-equal-of-cons-right
        (equal (intersectp-equal x (cons a y))
               (if (member-equal a x)
                   t (intersectp-equal x y))))

Basic set reasoning

Theorem: intersectp-of-self

(defthm intersectp-of-self
        (equal (intersectp x x) (consp x)))