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Fun-env

Fun-envp

Recognizer for fun-env.

Signature
(fun-envp x) → *

Definitions and Theorems

Function: fun-envp

(defun fun-envp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (identp (caar x))
         (fun-infop (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (fun-envp (cdr x)))))))

Theorem: booleanp-of-fun-envp

(defthm booleanp-of-fun-envp
  (booleanp (fun-envp x)))

Theorem: mapp-when-fun-envp

(defthm mapp-when-fun-envp
  (implies (fun-envp x) (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: fun-envp-of-tail

(defthm fun-envp-of-tail
  (implies (fun-envp x)
           (fun-envp (omap::tail x))))

Theorem: identp-of-head-key-when-fun-envp

(defthm identp-of-head-key-when-fun-envp
  (implies (and (fun-envp x)
                (not (omap::emptyp x)))
           (identp (mv-nth 0 (omap::head x)))))

Theorem: fun-infop-of-head-val-when-fun-envp

(defthm fun-infop-of-head-val-when-fun-envp
  (implies (and (fun-envp x)
                (not (omap::emptyp x)))
           (fun-infop (mv-nth 1 (omap::head x)))))

Theorem: fun-envp-of-update

(defthm fun-envp-of-update
  (implies (and (fun-envp x)
                (identp k)
                (fun-infop v))
           (fun-envp (omap::update k v x))))

Theorem: fun-envp-of-update*

(defthm fun-envp-of-update*
  (implies (and (fun-envp x) (fun-envp y))
           (fun-envp (omap::update* x y))))

Theorem: fun-envp-of-delete

(defthm fun-envp-of-delete
  (implies (fun-envp x)
           (fun-envp (omap::delete k x))))

Theorem: fun-envp-of-delete*

(defthm fun-envp-of-delete*
  (implies (fun-envp x)
           (fun-envp (omap::delete* k x))))

Theorem: identp-when-assoc-fun-envp-binds-free-x

(defthm identp-when-assoc-fun-envp-binds-free-x
  (implies (and (omap::assoc k x) (fun-envp x))
           (identp k)))

Theorem: identp-of-car-of-assoc-fun-envp

(defthm identp-of-car-of-assoc-fun-envp
  (implies (and (fun-envp x) (omap::assoc k x))
           (identp (car (omap::assoc k x)))))

Theorem: fun-infop-of-cdr-of-assoc-fun-envp

(defthm fun-infop-of-cdr-of-assoc-fun-envp
  (implies (and (fun-envp x) (omap::assoc k x))
           (fun-infop (cdr (omap::assoc k x)))))

Theorem: fun-infop-of-lookup-when-fun-envp

(defthm fun-infop-of-lookup-when-fun-envp
  (implies (and (fun-envp x) (omap::assoc k x))
           (fun-infop (omap::lookup k x))))