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Sd-filter-problems

Signature

(sd-filter-problems x major minor) → (mv major minor)

Arguments

x — Guard (sd-problemlist-p x).

major — Guard (sd-problemlist-p major).

minor — Guard (sd-problemlist-p minor).

Returns

major — Type (sd-problemlist-p major), given the guard.

minor — Type (sd-problemlist-p minor), given the guard.

Definitions and Theorems

Function: sd-filter-problems

(defun sd-filter-problems (x major minor)
  (declare (xargs :guard (and (sd-problemlist-p x)
                              (sd-problemlist-p major)
                              (sd-problemlist-p minor))))
  (let ((__function__ 'sd-filter-problems))
    (declare (ignorable __function__))
    (cond ((atom x) (mv major minor))
          ((sd-problem-major-p (car x))
           (sd-filter-problems (cdr x)
                               (cons (car x) major)
                               minor))
          (t (sd-filter-problems (cdr x)
                                 major (cons (car x) minor))))))

Theorem: sd-problemlist-p-of-sd-filter-problems.major

(defthm sd-problemlist-p-of-sd-filter-problems.major
  (implies (and (force (sd-problemlist-p x))
                (force (sd-problemlist-p major))
                (force (sd-problemlist-p minor)))
           (b* (((mv ?major ?minor)
                 (sd-filter-problems x major minor)))
             (sd-problemlist-p major)))
  :rule-classes :rewrite)

Theorem: sd-problemlist-p-of-sd-filter-problems.minor

(defthm sd-problemlist-p-of-sd-filter-problems.minor
  (implies (and (force (sd-problemlist-p x))
                (force (sd-problemlist-p major))
                (force (sd-problemlist-p minor)))
           (b* (((mv ?major ?minor)
                 (sd-filter-problems x major minor)))
             (sd-problemlist-p minor)))
  :rule-classes :rewrite)

Theorem: true-listp-sd-filter-problems

(defthm true-listp-sd-filter-problems
 (and
    (implies
         (true-listp major)
         (true-listp (mv-nth 0 (sd-filter-problems x major minor))))
    (implies
         (true-listp minor)
         (true-listp (mv-nth 1
                             (sd-filter-problems x major minor))))))