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Quantifier

Quantifierp

Recognizer for quantifier structures.

Signature
(quantifierp x) → *

Definitions and Theorems

Function: quantifierp

(defun quantifierp (x)
  (declare (xargs :guard t))
  (let ((__function__ 'quantifierp))
    (declare (ignorable __function__))
    (and (consp x)
         (cond ((or (atom x) (eq (car x) :forall))
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               (t (and (eq (car x) :exists)
                       (and (true-listp (cdr x))
                            (eql (len (cdr x)) 0))
                       (b* nil t)))))))

Theorem: consp-when-quantifierp

(defthm consp-when-quantifierp
  (implies (quantifierp x) (consp x))
  :rule-classes :compound-recognizer)