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Lhs.lisp

Lhs-override-vars

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

Definitions and Theorems

Function: lhs-override-vars

(defun lhs-override-vars (x)
  (declare (xargs :guard (lhs-override-p x)))
  (let ((__function__ 'lhs-override-vars))
    (declare (ignorable __function__))
    (b* (((lhs-override x)))
      (append (svex-vars x.test)
              (svex-vars x.val)))))

Theorem: svarlist-p-of-lhs-override-vars

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

Theorem: vars-of-lhs-override->test

(defthm vars-of-lhs-override->test
  (implies (not (member v (lhs-override-vars x)))
           (not (member v (svex-vars (lhs-override->test x))))))

Theorem: vars-of-lhs-override->val

(defthm vars-of-lhs-override->val
  (implies (not (member v (lhs-override-vars x)))
           (not (member v (svex-vars (lhs-override->val x))))))

Theorem: vars-of-lhs-override

(defthm vars-of-lhs-override
 (implies
    (and (not (member v (svex-vars test)))
         (not (member v (svex-vars val))))
    (not (member v
                 (lhs-override-vars (lhs-override lhs test val))))))

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

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

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

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