This is an ordinary defenum.
Function:
(defun fgl-toplevel-sat-check-mode-p (x) (declare (xargs :guard t)) (or (eq x 't) (eq x 'nil) (eq x ':insert)))
Theorem: type-when-fgl-toplevel-sat-check-mode-p
(defthm type-when-fgl-toplevel-sat-check-mode-p (implies (fgl-toplevel-sat-check-mode-p x) (symbolp x)) :rule-classes :compound-recognizer)