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• Utilities

Min-nats

Minimum member in a list of naturals.

Signature

(min-nats x) → *

Arguments

x — Guard (nat-listp x).

Typically you would only use this on non-empty lists, but as a reasonable default we say the minimum of the empty list is 0.

Definitions and Theorems

Function: min-nats

(defun min-nats (x)
       (declare (xargs :guard (nat-listp x)))
       (let ((__function__ 'min-nats))
            (declare (ignorable __function__))
            (cond ((atom x) 0)
                  ((atom (cdr x)) (lnfix (car x)))
                  (t (min (lnfix (car x))
                          (min-nats (cdr x)))))))

Theorem: natp-of-min-nats

(defthm natp-of-min-nats (natp (min-nats x))
        :rule-classes :type-prescription)

Theorem: min-nats-bound

(defthm min-nats-bound
        (implies (consp x)
                 (<= (min-nats x) (max-nats x)))
        :rule-classes ((:rewrite) (:linear)))