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Vcscope-dinfo

Vcscope-dinfop

Recognizer for vcscope-dinfo.

Signature
(vcscope-dinfop x) → *

Definitions and Theorems

Function: vcscope-dinfop

(defun vcscope-dinfop (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (identifierp (caar x))
         (var/const-dinfop (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (vcscope-dinfop (cdr x)))))))

Theorem: booleanp-of-vcscope-dinfop

(defthm booleanp-of-vcscope-dinfop
  (booleanp (vcscope-dinfop x)))

Theorem: mapp-when-vcscope-dinfop

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

Theorem: vcscope-dinfop-of-tail

(defthm vcscope-dinfop-of-tail
  (implies (vcscope-dinfop x)
           (vcscope-dinfop (omap::tail x))))

Theorem: identifierp-of-head-key-when-vcscope-dinfop

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

Theorem: var/const-dinfop-of-head-val-when-vcscope-dinfop

(defthm var/const-dinfop-of-head-val-when-vcscope-dinfop
  (implies (and (vcscope-dinfop x)
                (not (omap::emptyp x)))
           (var/const-dinfop (mv-nth 1 (omap::head x)))))

Theorem: vcscope-dinfop-of-update

(defthm vcscope-dinfop-of-update
  (implies (and (vcscope-dinfop x)
                (identifierp k)
                (var/const-dinfop v))
           (vcscope-dinfop (omap::update k v x))))

Theorem: vcscope-dinfop-of-update*

(defthm vcscope-dinfop-of-update*
  (implies (and (vcscope-dinfop x)
                (vcscope-dinfop y))
           (vcscope-dinfop (omap::update* x y))))

Theorem: vcscope-dinfop-of-delete

(defthm vcscope-dinfop-of-delete
  (implies (vcscope-dinfop x)
           (vcscope-dinfop (omap::delete k x))))

Theorem: vcscope-dinfop-of-delete*

(defthm vcscope-dinfop-of-delete*
  (implies (vcscope-dinfop x)
           (vcscope-dinfop (omap::delete* k x))))

Theorem: identifierp-when-assoc-vcscope-dinfop-binds-free-x

(defthm identifierp-when-assoc-vcscope-dinfop-binds-free-x
  (implies (and (omap::assoc k x)
                (vcscope-dinfop x))
           (identifierp k)))

Theorem: identifierp-of-car-of-assoc-vcscope-dinfop

(defthm identifierp-of-car-of-assoc-vcscope-dinfop
  (implies (and (vcscope-dinfop x)
                (omap::assoc k x))
           (identifierp (car (omap::assoc k x)))))

Theorem: var/const-dinfop-of-cdr-of-assoc-vcscope-dinfop

(defthm var/const-dinfop-of-cdr-of-assoc-vcscope-dinfop
  (implies (and (vcscope-dinfop x)
                (omap::assoc k x))
           (var/const-dinfop (cdr (omap::assoc k x)))))

Theorem: var/const-dinfop-of-lookup-when-vcscope-dinfop

(defthm var/const-dinfop-of-lookup-when-vcscope-dinfop
  (implies (and (vcscope-dinfop x)
                (omap::assoc k x))
           (var/const-dinfop (omap::lookup k x))))