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Character-any-map

Character-any-mapp

Recognizer for character-any-map.

Signature
(character-any-mapp x) → *

Definitions and Theorems

Function: character-any-mapp

(defun character-any-mapp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (characterp (caar x))
         (any-p (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (fast-<< (caar x) (caadr x))
                  (character-any-mapp (cdr x)))))))

Theorem: booleanp-of-character-any-mapp

(defthm booleanp-of-character-any-mapp
  (booleanp (character-any-mapp x)))

Theorem: mapp-when-character-any-mapp

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

Theorem: character-any-mapp-of-tail

(defthm character-any-mapp-of-tail
  (implies (character-any-mapp x)
           (character-any-mapp (omap::tail x))))

Theorem: characterp-of-head-key-when-character-any-mapp

(defthm characterp-of-head-key-when-character-any-mapp
  (implies (and (character-any-mapp x)
                (not (omap::emptyp x)))
           (characterp (mv-nth 0 (omap::head x)))))

Theorem: any-p-of-head-val-when-character-any-mapp

(defthm any-p-of-head-val-when-character-any-mapp
  (implies (and (character-any-mapp x)
                (not (omap::emptyp x)))
           (any-p (mv-nth 1 (omap::head x)))))

Theorem: character-any-mapp-of-update

(defthm character-any-mapp-of-update
  (implies (and (character-any-mapp x)
                (characterp k)
                (any-p v))
           (character-any-mapp (omap::update k v x))))

Theorem: character-any-mapp-of-update*

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

Theorem: character-any-mapp-of-delete

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

Theorem: character-any-mapp-of-delete*

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

Theorem: characterp-when-assoc-character-any-mapp-binds-free-x

(defthm characterp-when-assoc-character-any-mapp-binds-free-x
  (implies (and (omap::assoc k x)
                (character-any-mapp x))
           (characterp k)))

Theorem: characterp-of-car-of-assoc-character-any-mapp

(defthm characterp-of-car-of-assoc-character-any-mapp
  (implies (and (character-any-mapp x)
                (omap::assoc k x))
           (characterp (car (omap::assoc k x)))))

Theorem: any-p-of-cdr-of-assoc-character-any-mapp

(defthm any-p-of-cdr-of-assoc-character-any-mapp
  (implies (and (character-any-mapp x)
                (omap::assoc k x))
           (any-p (cdr (omap::assoc k x)))))

Theorem: any-p-of-lookup-when-character-any-mapp

(defthm any-p-of-lookup-when-character-any-mapp
  (implies (and (character-any-mapp x)
                (omap::assoc k x))
           (any-p (omap::lookup k x))))