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• Proposal-address-set-map

Proposal-address-set-mapp

Recognizer for proposal-address-set-map.

Signature

(proposal-address-set-mapp x) → *

Definitions and Theorems

Function: proposal-address-set-mapp

(defun proposal-address-set-mapp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (proposalp (caar x))
         (address-setp (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (proposal-address-set-mapp (cdr x)))))))

Theorem: booleanp-of-proposal-address-set-mapp

(defthm booleanp-of-proposal-address-set-mapp
  (booleanp (proposal-address-set-mapp x)))

Theorem: mapp-when-proposal-address-set-mapp

(defthm mapp-when-proposal-address-set-mapp
  (implies (proposal-address-set-mapp x)
           (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: proposal-address-set-mapp-of-tail

(defthm proposal-address-set-mapp-of-tail
  (implies (proposal-address-set-mapp x)
           (proposal-address-set-mapp (omap::tail x))))

Theorem: proposalp-of-head-key-when-proposal-address-set-mapp

(defthm proposalp-of-head-key-when-proposal-address-set-mapp
  (implies (and (proposal-address-set-mapp x)
                (not (omap::emptyp x)))
           (proposalp (mv-nth 0 (omap::head x)))))

Theorem: address-setp-of-head-val-when-proposal-address-set-mapp

(defthm address-setp-of-head-val-when-proposal-address-set-mapp
  (implies (and (proposal-address-set-mapp x)
                (not (omap::emptyp x)))
           (address-setp (mv-nth 1 (omap::head x)))))

Theorem: proposal-address-set-mapp-of-update

(defthm proposal-address-set-mapp-of-update
  (implies (and (proposal-address-set-mapp x)
                (proposalp k)
                (address-setp v))
           (proposal-address-set-mapp (omap::update k v x))))

Theorem: proposal-address-set-mapp-of-update*

(defthm proposal-address-set-mapp-of-update*
  (implies (and (proposal-address-set-mapp x)
                (proposal-address-set-mapp y))
           (proposal-address-set-mapp (omap::update* x y))))

Theorem: proposal-address-set-mapp-of-delete

(defthm proposal-address-set-mapp-of-delete
  (implies (proposal-address-set-mapp x)
           (proposal-address-set-mapp (omap::delete k x))))

Theorem: proposal-address-set-mapp-of-delete*

(defthm proposal-address-set-mapp-of-delete*
  (implies (proposal-address-set-mapp x)
           (proposal-address-set-mapp (omap::delete* k x))))

Theorem: proposalp-when-assoc-proposal-address-set-mapp-binds-free-x

(defthm proposalp-when-assoc-proposal-address-set-mapp-binds-free-x
  (implies (and (omap::assoc k x)
                (proposal-address-set-mapp x))
           (proposalp k)))

Theorem: proposalp-of-car-of-assoc-proposal-address-set-mapp

(defthm proposalp-of-car-of-assoc-proposal-address-set-mapp
  (implies (and (proposal-address-set-mapp x)
                (omap::assoc k x))
           (proposalp (car (omap::assoc k x)))))

Theorem: address-setp-of-cdr-of-assoc-proposal-address-set-mapp

(defthm address-setp-of-cdr-of-assoc-proposal-address-set-mapp
  (implies (and (proposal-address-set-mapp x)
                (omap::assoc k x))
           (address-setp (cdr (omap::assoc k x)))))

Theorem: address-setp-of-lookup-when-proposal-address-set-mapp

(defthm address-setp-of-lookup-when-proposal-address-set-mapp
  (implies (and (proposal-address-set-mapp x)
                (omap::assoc k x))
           (address-setp (omap::lookup k x))))