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• Address

Svarlist-addr-p-badguy

Signature

(svarlist-addr-p-badguy x) → badguy

Arguments

x — Guard (svarlist-p x).

Returns

badguy — Type (iff (svar-p badguy) badguy).

Definitions and Theorems

Function: svarlist-addr-p-badguy

(defun svarlist-addr-p-badguy (x)
  (declare (xargs :guard (svarlist-p x)))
  (let ((__function__ 'svarlist-addr-p-badguy))
    (declare (ignorable __function__))
    (if (atom x)
        (make-svar :name :not-an-address)
      (if (svar-addr-p (car x))
          (svarlist-addr-p-badguy (cdr x))
        (svar-fix (car x))))))

Theorem: return-type-of-svarlist-addr-p-badguy

(defthm return-type-of-svarlist-addr-p-badguy
  (b* ((badguy (svarlist-addr-p-badguy x)))
    (iff (svar-p badguy) badguy))
  :rule-classes :rewrite)

Theorem: svarlist-addr-p-badguy-not-addr-p

(defthm svarlist-addr-p-badguy-not-addr-p
  (not (svar-addr-p (svarlist-addr-p-badguy x))))

Theorem: svarlist-addr-p-by-badguy

(defthm svarlist-addr-p-by-badguy
  (implies (not (member (svarlist-addr-p-badguy x)
                        (svarlist-fix x)))
           (svarlist-addr-p x)))

Theorem: svarlist-addr-p-badguy-not-member-when-addr-p

(defthm svarlist-addr-p-badguy-not-member-when-addr-p
  (implies (and (svarlist-addr-p x) (svarlist-p x))
           (not (member (svarlist-addr-p-badguy y) x))))

Theorem: svarlist-addr-p-badguy-not-equal-svar-addr

(defthm svarlist-addr-p-badguy-not-equal-svar-addr
  (implies (svar-addr-p y)
           (not (equal (svarlist-addr-p-badguy x) y))))

Theorem: svarlist-addr-p-badguy-of-svarlist-fix-x

(defthm svarlist-addr-p-badguy-of-svarlist-fix-x
  (equal (svarlist-addr-p-badguy (svarlist-fix x))
         (svarlist-addr-p-badguy x)))

Theorem: svarlist-addr-p-badguy-svarlist-equiv-congruence-on-x

(defthm svarlist-addr-p-badguy-svarlist-equiv-congruence-on-x
  (implies (svarlist-equiv x x-equiv)
           (equal (svarlist-addr-p-badguy x)
                  (svarlist-addr-p-badguy x-equiv)))
  :rule-classes :congruence)