Existential and universal quantifiers.
Note that these are in the "ACL2" package.
This is an ordinary std::defenum.
Function:
(defun defun-sk-quantifier-p (x) (declare (xargs :guard t)) (or (eq x 'exists) (eq x 'forall)))
Theorem: type-when-defun-sk-quantifier-p
(defthm type-when-defun-sk-quantifier-p (implies (defun-sk-quantifier-p x) (if (symbolp x) (if (not (equal x 't)) (not (equal x 'nil)) 'nil) 'nil)) :rule-classes :compound-recognizer)