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Paths-all-exist-p

Do all of these paths exist?

Signature
(paths-all-exist-p paths &key (state 'state)) → (mv err ans new-state)
Arguments: paths — Guard (string-listp paths).
Returns: err — NIL on success, or an error msg on failure.; ans — Meaningful only when there is no error.
Type (booleanp ans).; new-state — Type (state-p1 new-state), given (force (state-p1 state)).

Definitions and Theorems

Function: paths-all-exist-p-fn

(defun paths-all-exist-p-fn (paths state)
  (declare (xargs :stobjs (state)))
  (declare (xargs :guard (string-listp paths)))
  (let ((__function__ 'paths-all-exist-p))
    (declare (ignorable __function__))
    (b* (((when (atom paths)) (mv nil t state))
         ((mv err ans1 state)
          (path-exists-p (car paths)))
         ((when err) (mv err nil state))
         ((unless ans1) (mv nil nil state)))
      (paths-all-exist-p (cdr paths)))))

Theorem: booleanp-of-paths-all-exist-p.ans

(defthm booleanp-of-paths-all-exist-p.ans
  (b* (((mv ?err ?ans ?new-state)
        (paths-all-exist-p-fn paths state)))
    (booleanp ans))
  :rule-classes :type-prescription)

Theorem: state-p1-of-paths-all-exist-p.new-state

(defthm state-p1-of-paths-all-exist-p.new-state
  (implies (force (state-p1 state))
           (b* (((mv ?err ?ans ?new-state)
                 (paths-all-exist-p-fn paths state)))
             (state-p1 new-state)))
  :rule-classes :rewrite)

Theorem: w-state-of-paths-all-exist-p

(defthm w-state-of-paths-all-exist-p
  (b* (((mv ?err ?ans ?new-state)
        (paths-all-exist-p-fn paths state)))
    (equal (w new-state) (w state))))