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Lhrange

Lhrange->w

Get the w field from a lhrange.

Signature
(lhrange->w x) → w
Arguments: x — Guard (lhrange-p x).
Returns: w — Type (posp w).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: lhrange->w$inline

(defun lhrange->w$inline (x)
  (declare (xargs :guard (lhrange-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'lhrange->w))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (pos-fix (if (and (consp x) (integerp (car x)))
                        (car x)
                      1)))
         :exec
         (if (and (consp x) (integerp (car x)))
             (car x)
           1))))

Theorem: posp-of-lhrange->w

(defthm posp-of-lhrange->w
  (b* ((w (lhrange->w$inline x)))
    (posp w))
  :rule-classes (:rewrite :type-prescription))

Theorem: lhrange->w$inline-of-lhrange-fix-x

(defthm lhrange->w$inline-of-lhrange-fix-x
  (equal (lhrange->w$inline (lhrange-fix x))
         (lhrange->w$inline x)))

Theorem: lhrange->w$inline-lhrange-equiv-congruence-on-x

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