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• Pigeon-hole

Every-bird-in-hole

Signature

(every-bird-in-hole bird max-hole) → clauses

Arguments

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

max-hole — Fixed.
    Guard (natp max-hole).

Returns

clauses — Every bird is in some hole.
    Type (lit-list-listp clauses).

Definitions and Theorems

Function: every-bird-in-hole

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

Theorem: lit-list-listp-of-every-bird-in-hole

(defthm lit-list-listp-of-every-bird-in-hole
  (b* ((clauses (every-bird-in-hole bird max-hole)))
    (lit-list-listp clauses))
  :rule-classes :rewrite)