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Value-map

Value-mapp

Recognizer for value-map.

Signature
(value-mapp x) → *

Definitions and Theorems

Theorem: booleanp-of-value-mapp

(defthm booleanp-of-value-mapp
  (booleanp (value-mapp x)))

Theorem: mapp-when-value-mapp

(defthm mapp-when-value-mapp
  (implies (value-mapp x) (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: value-mapp-of-tail

(defthm value-mapp-of-tail
  (implies (value-mapp x)
           (value-mapp (omap::tail x))))

Theorem: identifierp-of-head-key-when-value-mapp

(defthm identifierp-of-head-key-when-value-mapp
  (implies (and (value-mapp x)
                (not (omap::emptyp x)))
           (identifierp (mv-nth 0 (omap::head x)))))

Theorem: valuep-of-head-val-when-value-mapp

(defthm valuep-of-head-val-when-value-mapp
  (implies (and (value-mapp x)
                (not (omap::emptyp x)))
           (valuep (mv-nth 1 (omap::head x)))))

Theorem: value-mapp-of-update

(defthm value-mapp-of-update
  (implies (and (value-mapp x)
                (identifierp k)
                (valuep v))
           (value-mapp (omap::update k v x))))

Theorem: value-mapp-of-update*

(defthm value-mapp-of-update*
  (implies (and (value-mapp x) (value-mapp y))
           (value-mapp (omap::update* x y))))

Theorem: value-mapp-of-delete

(defthm value-mapp-of-delete
  (implies (value-mapp x)
           (value-mapp (omap::delete k x))))

Theorem: value-mapp-of-delete*

(defthm value-mapp-of-delete*
  (implies (value-mapp x)
           (value-mapp (omap::delete* k x))))

Theorem: identifierp-when-assoc-value-mapp-binds-free-x

(defthm identifierp-when-assoc-value-mapp-binds-free-x
  (implies (and (omap::assoc k x) (value-mapp x))
           (identifierp k)))

Theorem: identifierp-of-car-of-assoc-value-mapp

(defthm identifierp-of-car-of-assoc-value-mapp
  (implies (and (value-mapp x) (omap::assoc k x))
           (identifierp (car (omap::assoc k x)))))

Theorem: valuep-of-cdr-of-assoc-value-mapp

(defthm valuep-of-cdr-of-assoc-value-mapp
  (implies (and (value-mapp x) (omap::assoc k x))
           (valuep (cdr (omap::assoc k x)))))

Theorem: valuep-of-lookup-when-value-mapp

(defthm valuep-of-lookup-when-value-mapp
  (implies (and (value-mapp x) (omap::assoc k x))
           (valuep (omap::lookup k x))))