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• Svex-select

Svex-select-vars

Signature

(svex-select-vars x) → vars

Arguments

x — Guard (svex-select-p x).

Returns

vars — Type (svarlist-p vars).

Definitions and Theorems

Function: svex-select-vars

(defun svex-select-vars (x)
  (declare (xargs :guard (svex-select-p x)))
  (let ((__function__ 'svex-select-vars))
    (declare (ignorable __function__))
    (cons (svex-select-inner-var x)
          (svexlist-vars (svex-select->indices x)))))

Theorem: svarlist-p-of-svex-select-vars

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

Theorem: svexlist-vars-of-svex-select->indices

(defthm svexlist-vars-of-svex-select->indices
  (implies (not (member v (svex-select-vars x)))
           (not (member v
                        (svexlist-vars (svex-select->indices x))))))

Theorem: svex-select-not-inner-var-when-not-member-select-vars

(defthm svex-select-not-inner-var-when-not-member-select-vars
  (implies (not (member v (svex-select-vars x)))
           (not (equal v (svex-select-inner-var x)))))

Theorem: svex-select-vars-of-replace-indices

(defthm svex-select-vars-of-replace-indices
 (implies
  (and (not (equal v (svex-select-inner-var x)))
       (not (member v (svexlist-vars indices))))
  (not
   (member
      v
      (svex-select-vars (svex-select-replace-indices x indices))))))

Theorem: svex-vars-of-svex-select-to-svex

(defthm svex-vars-of-svex-select-to-svex
  (implies (not (member v (svex-select-vars x)))
           (not (member v
                        (svex-vars (svex-select-to-svex x))))))

Theorem: svex-vars-of-svex-select-to-svex-with-substitution

(defthm svex-vars-of-svex-select-to-svex-with-substitution
 (implies
  (and (not (member v (svex-select-vars x)))
       (not (member v (svex-vars subst))))
  (not
   (member
     v
     (svex-vars (svex-select-to-svex-with-substitution x subst))))))

Theorem: svex-select-vars-of-svex-select-fix-x

(defthm svex-select-vars-of-svex-select-fix-x
  (equal (svex-select-vars (svex-select-fix x))
         (svex-select-vars x)))

Theorem: svex-select-vars-svex-select-equiv-congruence-on-x

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