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Svtv-override-triplemap-relevant-vars

Signature

(svtv-override-triplemap-relevant-vars triplemap spec) → vars

Arguments

triplemap — Guard (svtv-override-triplemap-p triplemap).

spec — Guard (svex-env-p spec).

Returns

vars — Type (svarlist-p vars).

Definitions and Theorems

Function: svtv-override-triplemap-relevant-vars

(defun svtv-override-triplemap-relevant-vars (triplemap spec)
 (declare (xargs :guard (and (svtv-override-triplemap-p triplemap)
                             (svex-env-p spec))))
 (let ((__function__ 'svtv-override-triplemap-relevant-vars))
  (declare (ignorable __function__))
  (if (atom triplemap)
      nil
   (append (and (mbt (and (consp (car triplemap))
                          (svar-p (caar triplemap))))
                (svtv-override-triple-relevant-vars (cdar triplemap)
                                                    spec))
           (svtv-override-triplemap-relevant-vars (cdr triplemap)
                                                  spec)))))

Theorem: svarlist-p-of-svtv-override-triplemap-relevant-vars

(defthm svarlist-p-of-svtv-override-triplemap-relevant-vars
 (b* ((vars (svtv-override-triplemap-relevant-vars triplemap spec)))
   (svarlist-p vars))
 :rule-classes :rewrite)

Theorem: svtv-override-triplemap-relevant-vars-correct

(defthm svtv-override-triplemap-relevant-vars-correct
 (implies
   (subsetp-equal
        (svtv-override-triplemap-relevant-vars triplemap spec)
        (svarlist-fix vars))
   (equal (svtv-override-triplemap-envs-match
               triplemap (svex-env-reduce vars env)
               spec)
          (svtv-override-triplemap-envs-match triplemap env spec))))

Theorem: svtv-override-triplemap-relevant-vars-of-svtv-override-triplemap-fix-triplemap

(defthm
 svtv-override-triplemap-relevant-vars-of-svtv-override-triplemap-fix-triplemap
 (equal (svtv-override-triplemap-relevant-vars
             (svtv-override-triplemap-fix triplemap)
             spec)
        (svtv-override-triplemap-relevant-vars triplemap spec)))

Theorem: svtv-override-triplemap-relevant-vars-svtv-override-triplemap-equiv-congruence-on-triplemap

(defthm
 svtv-override-triplemap-relevant-vars-svtv-override-triplemap-equiv-congruence-on-triplemap
 (implies
  (svtv-override-triplemap-equiv triplemap triplemap-equiv)
  (equal
      (svtv-override-triplemap-relevant-vars triplemap spec)
      (svtv-override-triplemap-relevant-vars triplemap-equiv spec)))
 :rule-classes :congruence)

Theorem: svtv-override-triplemap-relevant-vars-of-svex-env-fix-spec

(defthm svtv-override-triplemap-relevant-vars-of-svex-env-fix-spec
  (equal (svtv-override-triplemap-relevant-vars
              triplemap (svex-env-fix spec))
         (svtv-override-triplemap-relevant-vars triplemap spec)))

Theorem: svtv-override-triplemap-relevant-vars-svex-env-equiv-congruence-on-spec

(defthm
 svtv-override-triplemap-relevant-vars-svex-env-equiv-congruence-on-spec
 (implies
  (svex-env-equiv spec spec-equiv)
  (equal
      (svtv-override-triplemap-relevant-vars triplemap spec)
      (svtv-override-triplemap-relevant-vars triplemap spec-equiv)))
 :rule-classes :congruence)