File: union.lisp

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; Standard Lists Library
;
; Copyright (C) 2019 Kestrel Institute (http://www.kestrel.edu)
;
; License: A 3-clause BSD license. See the LICENSE file distributed with ACL2.
;
; Author: Alessandro Coglio (coglio@kestrel.edu)

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(in-package "ACL2")

(include-book "xdoc/top" :dir :system)

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(defsection std/lists/union
  :parents (std/lists union$)
  :short "Theorems about @(tsee union$) in the @(see std/lists) library."

  (defthm true-listp-of-union-equal
    (equal (true-listp (union-equal x y))
           (true-listp y)))

  (defthm true-listp-of-union-equal-type
    (implies (true-listp y)
             (true-listp (union-equal x y)))
    :rule-classes :type-prescription))

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(in-theory (disable union-equal))