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Quantifier

Quantifier-kind

Get the kind (tag) of a quantifier structure.

Signature
(quantifier-kind x) → kind
Arguments: x — Guard (quantifierp x).

Definitions and Theorems

Function: quantifier-kind$inline

(defun quantifier-kind$inline (x)
  (declare (xargs :guard (quantifierp x)))
  (let ((__function__ 'quantifier-kind))
    (declare (ignorable __function__))
    (mbe :logic (cond ((or (atom x) (eq (car x) :forall))
                       :forall)
                      (t :exists))
         :exec (car x))))

Theorem: quantifier-kind-possibilities

(defthm quantifier-kind-possibilities
  (or (equal (quantifier-kind x) :forall)
      (equal (quantifier-kind x) :exists))
  :rule-classes
  ((:forward-chaining :trigger-terms ((quantifier-kind x)))))