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Omaps

Size

Size of an omap.

Signature
(size map) → size
Arguments: map — Guard (mapp map).
Returns: size — Type (natp size).

This is the number of keys in the omap.

The unfold-...-size-const are useful to turn assertions about sizes and constants into assertions about emptyp and tail; the expansion terminates because of the syntaxp restriction. These theorems are disabled by default. These are the omap analogous of these theorems for lists.

Definitions and Theorems

Function: size

(defun size (map)
  (declare (xargs :guard (mapp map)))
  (let ((__function__ 'size))
    (declare (ignorable __function__))
    (cond ((emptyp map) 0)
          (t (1+ (size (tail map)))))))

Theorem: natp-of-size

(defthm natp-of-size
  (b* ((size (size map))) (natp size))
  :rule-classes :rewrite)

Theorem: unfold-equal-size-const

(defthm unfold-equal-size-const
  (implies (syntaxp (quotep c))
           (equal (equal (size map) c)
                  (if (natp c)
                      (if (equal c 0)
                          (emptyp map)
                        (and (not (emptyp map))
                             (equal (size (tail map)) (1- c))))
                    nil))))

Theorem: unfold-gteq-size-const

(defthm unfold-gteq-size-const
  (implies (syntaxp (quotep c))
           (equal (>= (size map) c)
                  (or (<= (fix c) 0)
                      (and (not (emptyp map))
                           (>= (size (tail map)) (1- c)))))))

Theorem: unfold-gt-size-const

(defthm unfold-gt-size-const
  (implies (syntaxp (quotep c))
           (equal (> (size map) c)
                  (or (< (fix c) 0)
                      (and (not (emptyp map))
                           (> (size (tail map)) (1- c)))))))

Theorem: size-to-cardinality-of-keys

(defthm size-to-cardinality-of-keys
  (equal (size map)
         (cardinality (keys map))))

Theorem: cardinality-of-keys-to-size

(defthm cardinality-of-keys-to-size
  (equal (cardinality (keys map))
         (size map)))