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• Pigeon-hole

No-others-in-hole

Signature

(no-others-in-hole tweety birds hole) → clauses

Arguments

tweety — Fixed.
    Guard (natp tweety).

birds — Counts down from max birds.
    Guard (natp birds).

hole — Fixed.
    Guard (natp hole).

Returns

clauses — No other bird shares hole with tweety.
    Type (lit-list-listp clauses).

Definitions and Theorems

Function: no-others-in-hole

(defun no-others-in-hole (tweety birds hole)
  (declare (xargs :guard (and (natp tweety)
                              (natp birds)
                              (natp hole))))
  (let ((__function__ 'no-others-in-hole))
    (declare (ignorable __function__))
    (b* (((when (zp birds)) nil)
         (birds (- birds 1))
         ((when (eql tweety birds))
          (no-others-in-hole tweety birds hole)))
      (cons (not-both-in-hole tweety birds hole)
            (no-others-in-hole tweety birds hole)))))

Theorem: lit-list-listp-of-no-others-in-hole

(defthm lit-list-listp-of-no-others-in-hole
  (b* ((clauses (no-others-in-hole tweety birds hole)))
    (lit-list-listp clauses))
  :rule-classes :rewrite)