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Omaps

Delete*

Remove keys, and associated values, from an omap.

Signature
(delete* keys map) → map1
Arguments: keys — Guard (setp keys).; map — Guard (mapp map).
Returns: map1 — Type (mapp map1).

This lifts delete from a single key to a set of keys.

Definitions and Theorems

Function: delete*

(defun delete* (keys map)
  (declare (xargs :guard (and (setp keys) (mapp map))))
  (let ((__function__ 'delete*))
    (declare (ignorable __function__))
    (cond ((set::emptyp keys) (mfix map))
          (t (delete (set::head keys)
                     (delete* (set::tail keys) map))))))

Theorem: mapp-of-delete*

(defthm mapp-of-delete*
  (b* ((map1 (delete* keys map)))
    (mapp map1))
  :rule-classes :rewrite)

Theorem: delete*-when-left-emptyp

(defthm delete*-when-left-emptyp
  (implies (set::emptyp keys)
           (equal (delete* keys map) (mfix map))))

Theorem: delete*-when-right-emptyp

(defthm delete*-when-right-emptyp
  (implies (emptyp map)
           (equal (delete* keys map) nil)))