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Initialization

System-init-loop

Signature
(system-init-loop correct-vals valmap) → new-valmap
Arguments: correct-vals — Guard (address-setp correct-vals).; valmap — Guard (address-validator-state-mapp valmap).
Returns: new-valmap — Type (address-validator-state-mapp new-valmap), given (address-validator-state-mapp valmap).

Definitions and Theorems

Function: system-init-loop

(defun system-init-loop (correct-vals valmap)
  (declare
       (xargs :guard (and (address-setp correct-vals)
                          (address-validator-state-mapp valmap))))
  (let ((__function__ 'system-init-loop))
    (declare (ignorable __function__))
    (b* (((when (emptyp (address-set-fix correct-vals)))
          (address-validator-state-map-fix valmap))
         (valmap (omap::update (head correct-vals)
                               (validator-init)
                               valmap)))
      (system-init-loop (tail correct-vals)
                        valmap))))

Theorem: address-validator-state-mapp-of-system-init-loop

(defthm address-validator-state-mapp-of-system-init-loop
  (implies (address-validator-state-mapp valmap)
           (b* ((new-valmap (system-init-loop correct-vals valmap)))
             (address-validator-state-mapp new-valmap)))
  :rule-classes :rewrite)

Theorem: system-init-loop-of-address-set-fix-correct-vals

(defthm system-init-loop-of-address-set-fix-correct-vals
  (equal (system-init-loop (address-set-fix correct-vals)
                           valmap)
         (system-init-loop correct-vals valmap)))

Theorem: system-init-loop-address-set-equiv-congruence-on-correct-vals

(defthm
      system-init-loop-address-set-equiv-congruence-on-correct-vals
  (implies (address-set-equiv correct-vals correct-vals-equiv)
           (equal (system-init-loop correct-vals valmap)
                  (system-init-loop correct-vals-equiv valmap)))
  :rule-classes :congruence)

Theorem: in-of-keys-of-system-init-loop

(defthm in-of-keys-of-system-init-loop
 (implies
     (address-validator-state-mapp valmap)
     (equal (in val
                (omap::keys (system-init-loop correct-vals valmap)))
            (or (in val (address-set-fix correct-vals))
                (in val (omap::keys valmap))))))

Theorem: keys-of-system-init-loop

(defthm keys-of-system-init-loop
 (implies (address-validator-state-mapp valmap)
          (equal (omap::keys (system-init-loop correct-vals valmap))
                 (union (address-set-fix correct-vals)
                        (omap::keys valmap)))))

Theorem: lookup-of-system-init-loop

(defthm lookup-of-system-init-loop
  (implies
       (address-validator-state-mapp valmap)
       (equal (omap::lookup val
                            (system-init-loop correct-vals valmap))
              (if (in val (address-set-fix correct-vals))
                  (validator-init)
                (omap::lookup val valmap)))))