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• Pigeon-hole

Bird-in-some-hole

Signature

(bird-in-some-hole bird hole) → clause

Arguments

bird — Fixed.
    Guard (natp bird).

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

Returns

clause — This bird is in some hole.
    Type (lit-listp clause).

Definitions and Theorems

Function: bird-in-some-hole

(defun bird-in-some-hole (bird hole)
  (declare (xargs :guard (and (natp bird) (natp hole))))
  (let ((__function__ 'bird-in-some-hole))
    (declare (ignorable __function__))
    (b* (((when (zp hole)) nil)
         (hole (- hole 1)))
      (cons (bird-in-hole bird hole)
            (bird-in-some-hole bird hole)))))

Theorem: lit-listp-of-bird-in-some-hole

(defthm lit-listp-of-bird-in-some-hole
  (b* ((clause (bird-in-some-hole bird hole)))
    (lit-listp clause))
  :rule-classes :rewrite)