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Lhs.lisp

Lhspairs-vars

Signature
(lhspairs-vars x) → vars
Arguments: x — Guard (lhspairs-p x).
Returns: vars — Type (svarlist-p vars).

Definitions and Theorems

Function: lhspairs-vars

(defun lhspairs-vars (x)
  (declare (xargs :guard (lhspairs-p x)))
  (let ((__function__ 'lhspairs-vars))
    (declare (ignorable __function__))
    (b* ((x (lhspairs-fix x)))
      (if (atom x)
          nil
        (append (lhs-vars (caar x))
                (lhs-vars (cdar x))
                (lhspairs-vars (cdr x)))))))

Theorem: svarlist-p-of-lhspairs-vars

(defthm svarlist-p-of-lhspairs-vars
  (b* ((vars (lhspairs-vars x)))
    (svarlist-p vars))
  :rule-classes :rewrite)

Theorem: lhspairs-vars-of-lhspairs-fix-x

(defthm lhspairs-vars-of-lhspairs-fix-x
  (equal (lhspairs-vars (lhspairs-fix x))
         (lhspairs-vars x)))

Theorem: lhspairs-vars-lhspairs-equiv-congruence-on-x

(defthm lhspairs-vars-lhspairs-equiv-congruence-on-x
  (implies (lhspairs-equiv x x-equiv)
           (equal (lhspairs-vars x)
                  (lhspairs-vars x-equiv)))
  :rule-classes :congruence)