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Lhs.lisp

Svar-map-vars

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

Definitions and Theorems

Function: svar-map-vars

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

Theorem: svarlist-p-of-svar-map-vars

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

Theorem: svar-map-vars-of-svar-map-fix-x

(defthm svar-map-vars-of-svar-map-fix-x
  (equal (svar-map-vars (svar-map-fix x))
         (svar-map-vars x)))

Theorem: svar-map-vars-svar-map-equiv-congruence-on-x

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