		Search-engine friendly clone of the ACL2 documentation.

Lhs.lisp

Lhs-vars

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

Definitions and Theorems

Function: lhs-vars

(defun lhs-vars (x)
  (declare (xargs :guard (lhs-p x)))
  (let ((__function__ 'lhs-vars))
    (declare (ignorable __function__))
    (b* (((when (atom x)) nil)
         ((lhrange first) (car x)))
      (append (lhatom-vars first.atom)
              (lhs-vars (cdr x))))))

Theorem: svarlist-p-of-lhs-vars

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

Theorem: lhs-vars-of-cons

(defthm lhs-vars-of-cons
  (equal (lhs-vars (cons a b))
         (append (lhatom-vars (lhrange->atom a))
                 (lhs-vars b))))

Theorem: lhs-vars-when-consp

(defthm lhs-vars-when-consp
  (implies (consp x)
           (equal (lhs-vars x)
                  (append (lhatom-vars (lhrange->atom (car x)))
                          (lhs-vars (cdr x)))))
  :rule-classes ((:rewrite :backchain-limit-lst 0)))

Theorem: lhs-vars-of-lhs-fix-x

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

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

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

Theorem: vars-of-lhs-cons

(defthm vars-of-lhs-cons
  (iff (member v (lhs-vars (lhs-cons a b)))
       (or (member v (lhs-vars b))
           (member v (lhatom-vars (lhrange->atom a))))))

Theorem: vars-of-lhs-norm

(defthm vars-of-lhs-norm
  (iff (member v (lhs-vars (lhs-norm x)))
       (member v (lhs-vars x))))

Theorem: vars-of-lhs-concat

(defthm vars-of-lhs-concat
  (implies (and (not (member v (lhs-vars x)))
                (not (member v (lhs-vars y))))
           (not (member v (lhs-vars (lhs-concat w x y))))))

Theorem: vars-of-lhs-rsh

(defthm vars-of-lhs-rsh
  (implies (not (member v (lhs-vars x)))
           (not (member v (lhs-vars (lhs-rsh sh x))))))