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• Pigeon-hole

No-two-in-any-hole

Signature

(no-two-in-any-hole max-birds hole) → clauses

Arguments

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

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

Returns

clauses — No two birds share any hole.
    Type (lit-list-listp clauses).

Definitions and Theorems

Function: no-two-in-any-hole

(defun no-two-in-any-hole (max-birds hole)
  (declare (xargs :guard (and (natp max-birds) (natp hole))))
  (let ((__function__ 'no-two-in-any-hole))
    (declare (ignorable __function__))
    (b* (((when (zp hole)) nil)
         (hole (- hole 1)))
      (append (no-two-in-hole max-birds hole)
              (no-two-in-any-hole max-birds hole)))))

Theorem: lit-list-listp-of-no-two-in-any-hole

(defthm lit-list-listp-of-no-two-in-any-hole
  (b* ((clauses (no-two-in-any-hole max-birds hole)))
    (lit-list-listp clauses))
  :rule-classes :rewrite)