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Lhs.lisp

Lhs-width

Signature
(lhs-width x) → w
Arguments: x — Guard (lhs-p x).
Returns: w — Type (natp w).

Definitions and Theorems

Function: lhs-width

(defun lhs-width (x)
  (declare (xargs :guard (lhs-p x)))
  (let ((__function__ 'lhs-width))
    (declare (ignorable __function__))
    (if (atom x)
        0
      (+ (lhrange->w (car x))
         (lhs-width (cdr x))))))

Theorem: natp-of-lhs-width

(defthm natp-of-lhs-width
  (b* ((w (lhs-width x))) (natp w))
  :rule-classes :type-prescription)

Theorem: lhs-width-of-lhs-fix-x

(defthm lhs-width-of-lhs-fix-x
  (equal (lhs-width (lhs-fix x))
         (lhs-width x)))

Theorem: lhs-width-lhs-equiv-congruence-on-x

(defthm lhs-width-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (lhs-width x)
                  (lhs-width x-equiv)))
  :rule-classes :congruence)

Theorem: lhs-width-bounds-eval-width

(defthm lhs-width-bounds-eval-width
  (equal (4vec-concat (2vec (lhs-width x))
                      (lhs-eval x env)
                      (4vec-z))
         (lhs-eval x env)))