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Range

Range->lsb

Get the lsb field from a range.

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

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: range->lsb$inline

(defun range->lsb$inline (x)
  (declare (xargs :guard (range-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'range->lsb))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (nfix (std::prod-car x)))
         :exec (std::prod-car x))))

Theorem: natp-of-range->lsb

(defthm natp-of-range->lsb
  (b* ((lsb (range->lsb$inline x)))
    (natp lsb))
  :rule-classes :type-prescription)

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

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

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

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