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Symbolic-arithmetic

All-nil

Signature
(all-nil x) → *

Definitions and Theorems

Function: all-nil

(defun all-nil (x)
  (declare (xargs :guard t))
  (let ((__function__ 'all-nil))
    (declare (ignorable __function__))
    (if (atom x)
        t
      (and (eq (car x) nil)
           (all-nil (cdr x))))))

Theorem: all-nil-when-atom

(defthm all-nil-when-atom
  (implies (atom x) (all-nil x)))

Theorem: zero-when-all-nil

(defthm zero-when-all-nil
  (implies (all-nil x)
           (equal (bfr-list->u x env) 0)))