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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)))