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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)))

Theorem: delete*-of-mfix-map

(defthm delete*-of-mfix-map
  (equal (delete* keys (mfix map))
         (delete* keys map)))

Theorem: delete*-mequiv-congruence-on-map

(defthm delete*-mequiv-congruence-on-map
  (implies (mequiv map map-equiv)
           (equal (delete* keys map)
                  (delete* keys map-equiv)))
  :rule-classes :congruence)