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Pigeon-hole

Signature

(pigeon-hole num-birds num-holes) → clauses

Arguments

num-birds — Guard (natp num-birds).

num-holes — Guard (natp num-holes).

Returns

clauses — Type (lit-list-listp clauses).

Definitions and Theorems

Function: pigeon-hole

(defun pigeon-hole (num-birds num-holes)
  (declare (xargs :guard (and (natp num-birds)
                              (natp num-holes))))
  (let ((__function__ 'pigeon-hole))
    (declare (ignorable __function__))
    (append (every-bird-in-hole num-birds num-holes)
            (no-two-in-any-hole num-birds num-holes))))

Theorem: lit-list-listp-of-pigeon-hole

(defthm lit-list-listp-of-pigeon-hole
  (b* ((clauses (pigeon-hole num-birds num-holes)))
    (lit-list-listp clauses))
  :rule-classes :rewrite)

Subtopics

No-two-in-hole-aux

No-others-in-hole

Not-both-in-hole

No-two-in-any-hole

Every-bird-in-hole

No-two-in-hole

Bird-in-some-hole

Bird-in-hole