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Sign

Signp

Recognizer for sign structures.

Signature
(signp x) → *

Definitions and Theorems

Function: signp

(defun signp (x)
  (declare (xargs :guard t))
  (and (consp x)
       (cond ((or (atom x) (eq (car x) :plus))
              (and (eq (cdr x) nil) (b* nil t)))
             (t (and (eq (car x) :minus)
                     (and (eq (cdr x) nil))
                     (b* nil t))))))

Theorem: consp-when-signp

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