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• Bfr

Bfr-listp-witness

Signature

(bfr-listp-witness x bfrstate) → *

Arguments

bfrstate — Guard (bfrstate-p bfrstate).

Definitions and Theorems

Function: bfr-listp-witness

(defun bfr-listp-witness (x bfrstate)
  (declare (xargs :guard (bfrstate-p bfrstate)))
  (let ((__function__ 'bfr-listp-witness))
    (declare (ignorable __function__))
    (if (atom x)
        'not-a-bfr
      (if (bfr-p (car x))
          (bfr-listp-witness (cdr x) bfrstate)
        (car x)))))

Theorem: bfr-listp-witness-nonnil

(defthm bfr-listp-witness-nonnil
  (bfr-listp-witness x bfrstate))

Theorem: bfr-listp-witness-not-bfr-p

(defthm bfr-listp-witness-not-bfr-p
  (not (bfr-p (bfr-listp-witness x bfrstate)
              bfrstate)))

Theorem: bfr-listp-when-not-member-witness

(defthm bfr-listp-when-not-member-witness
  (implies (not (member (bfr-listp-witness x bfrstate)
                        x))
           (bfr-listp x bfrstate)))

Theorem: not-member-bfr-listp-witness-when-bfr-listp

(defthm not-member-bfr-listp-witness-when-bfr-listp
  (implies (bfr-listp x bfrstate)
           (not (member (bfr-listp-witness y bfrstate)
                        x))))

Theorem: bfr-listp-witness-of-bfrstate-fix-bfrstate

(defthm bfr-listp-witness-of-bfrstate-fix-bfrstate
  (equal (bfr-listp-witness x (bfrstate-fix bfrstate))
         (bfr-listp-witness x bfrstate)))

Theorem: bfr-listp-witness-bfrstate-equiv-congruence-on-bfrstate

(defthm bfr-listp-witness-bfrstate-equiv-congruence-on-bfrstate
  (implies (bfrstate-equiv bfrstate bfrstate-equiv)
           (equal (bfr-listp-witness x bfrstate)
                  (bfr-listp-witness x bfrstate-equiv)))
  :rule-classes :congruence)