• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
    • Std/lists
    • Std/alists
    • Obags
      • Bagp
      • Bag
      • Tail
      • Head
      • Emptyp
      • Subbag
      • Intersect
      • Union
      • Insert
      • Difference
      • Delete
      • Cardinality
      • Bfix
      • In
      • Occs
    • Std/util
    • Std/strings
    • Std/osets
    • Std/io
    • Std/basic
    • Std/system
    • Std/typed-lists
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Obags

Intersect

Intersection of all (the occurrences of) all the elements of two obags.

Signature

(intersect bag1 bag2) → bag

Arguments

bag1 — Guard (bagp bag1).

bag2 — Guard (bagp bag2).

Returns

bag — Type (bagp bag).

This is similar to set::intersect for osets.

Definitions and Theorems

Function: intersect

(defun intersect (bag1 bag2)
  (declare (xargs :guard (and (bagp bag1) (bagp bag2))))
  (let ((__function__ 'intersect))
    (declare (ignorable __function__))
    (cond ((emptyp bag1) nil)
          ((in (head bag1) bag2)
           (insert (head bag1)
                   (intersect (tail bag1) bag2)))
          (t (intersect (tail bag1) bag2)))))

Theorem: bagp-of-intersect

(defthm bagp-of-intersect
  (b* ((bag (intersect bag1 bag2)))
    (bagp bag))
  :rule-classes :rewrite)