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• Ident-paramdecl-map

Ident-paramdecl-mapp

Recognizer for ident-paramdecl-map.

Signature

(ident-paramdecl-mapp x) → *

Definitions and Theorems

Function: ident-paramdecl-mapp

(defun ident-paramdecl-mapp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (identp (caar x))
         (paramdeclp (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (ident-paramdecl-mapp (cdr x)))))))

Theorem: booleanp-of-ident-paramdecl-mapp

(defthm booleanp-of-ident-paramdecl-mapp
  (booleanp (ident-paramdecl-mapp x)))

Theorem: mapp-when-ident-paramdecl-mapp

(defthm mapp-when-ident-paramdecl-mapp
  (implies (ident-paramdecl-mapp x)
           (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: ident-paramdecl-mapp-of-tail

(defthm ident-paramdecl-mapp-of-tail
  (implies (ident-paramdecl-mapp x)
           (ident-paramdecl-mapp (omap::tail x))))

Theorem: identp-of-head-key-when-ident-paramdecl-mapp

(defthm identp-of-head-key-when-ident-paramdecl-mapp
  (implies (and (ident-paramdecl-mapp x)
                (not (omap::emptyp x)))
           (identp (mv-nth 0 (omap::head x)))))

Theorem: paramdeclp-of-head-val-when-ident-paramdecl-mapp

(defthm paramdeclp-of-head-val-when-ident-paramdecl-mapp
  (implies (and (ident-paramdecl-mapp x)
                (not (omap::emptyp x)))
           (paramdeclp (mv-nth 1 (omap::head x)))))

Theorem: ident-paramdecl-mapp-of-update

(defthm ident-paramdecl-mapp-of-update
  (implies (and (ident-paramdecl-mapp x)
                (identp k)
                (paramdeclp v))
           (ident-paramdecl-mapp (omap::update k v x))))

Theorem: ident-paramdecl-mapp-of-update*

(defthm ident-paramdecl-mapp-of-update*
  (implies (and (ident-paramdecl-mapp x)
                (ident-paramdecl-mapp y))
           (ident-paramdecl-mapp (omap::update* x y))))

Theorem: ident-paramdecl-mapp-of-delete

(defthm ident-paramdecl-mapp-of-delete
  (implies (ident-paramdecl-mapp x)
           (ident-paramdecl-mapp (omap::delete k x))))

Theorem: ident-paramdecl-mapp-of-delete*

(defthm ident-paramdecl-mapp-of-delete*
  (implies (ident-paramdecl-mapp x)
           (ident-paramdecl-mapp (omap::delete* k x))))

Theorem: identp-when-assoc-ident-paramdecl-mapp-binds-free-x

(defthm identp-when-assoc-ident-paramdecl-mapp-binds-free-x
  (implies (and (omap::assoc k x)
                (ident-paramdecl-mapp x))
           (identp k)))

Theorem: identp-of-car-of-assoc-ident-paramdecl-mapp

(defthm identp-of-car-of-assoc-ident-paramdecl-mapp
  (implies (and (ident-paramdecl-mapp x)
                (omap::assoc k x))
           (identp (car (omap::assoc k x)))))

Theorem: paramdeclp-of-cdr-of-assoc-ident-paramdecl-mapp

(defthm paramdeclp-of-cdr-of-assoc-ident-paramdecl-mapp
  (implies (and (ident-paramdecl-mapp x)
                (omap::assoc k x))
           (paramdeclp (cdr (omap::assoc k x)))))

Theorem: paramdeclp-of-lookup-when-ident-paramdecl-mapp

(defthm paramdeclp-of-lookup-when-ident-paramdecl-mapp
  (implies (and (ident-paramdecl-mapp x)
                (omap::assoc k x))
           (paramdeclp (omap::lookup k x))))