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Range

Range->width

Get the width field from a range.

Signature
(range->width x) → width
Arguments: x — Guard (range-p x).
Returns: width — Type (maybe-posp width).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: range->width$inline

(defun range->width$inline (x)
  (declare (xargs :guard (range-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'range->width))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (acl2::maybe-posp-fix (std::prod-cdr x)))
         :exec (std::prod-cdr x))))

Theorem: maybe-posp-of-range->width

(defthm maybe-posp-of-range->width
  (b* ((width (range->width$inline x)))
    (maybe-posp width))
  :rule-classes :type-prescription)

Theorem: range->width$inline-of-range-fix-x

(defthm range->width$inline-of-range-fix-x
  (equal (range->width$inline (range-fix x))
         (range->width$inline x)))

Theorem: range->width$inline-range-equiv-congruence-on-x

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