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Num-val-range

Num-val-range->min

Get the min field from a num-val-range.

Signature
(num-val-range->min x) → min
Arguments: x — Guard (num-val-p x).
Returns: min — Type (natp min).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: num-val-range->min$inline

(defun num-val-range->min$inline (x)
  (declare (xargs :guard (num-val-p x)))
  (declare (xargs :guard (equal (num-val-kind x) :range)))
  (let ((__function__ 'num-val-range->min))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (num-val-kind x) :range)
                      x)))
           (nfix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: natp-of-num-val-range->min

(defthm natp-of-num-val-range->min
  (b* ((min (num-val-range->min$inline x)))
    (natp min))
  :rule-classes :rewrite)

Theorem: num-val-range->min$inline-of-num-val-fix-x

(defthm num-val-range->min$inline-of-num-val-fix-x
  (equal (num-val-range->min$inline (num-val-fix x))
         (num-val-range->min$inline x)))

Theorem: num-val-range->min$inline-num-val-equiv-congruence-on-x

(defthm num-val-range->min$inline-num-val-equiv-congruence-on-x
  (implies (num-val-equiv x x-equiv)
           (equal (num-val-range->min$inline x)
                  (num-val-range->min$inline x-equiv)))
  :rule-classes :congruence)

Theorem: num-val-range->min-when-wrong-kind

(defthm num-val-range->min-when-wrong-kind
  (implies (not (equal (num-val-kind x) :range))
           (equal (num-val-range->min x)
                  (nfix nil))))