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Svtv-override-triple-relevant-vars

Signature

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

Arguments

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

spec — Guard (svex-env-p spec).

Returns

vars — Type (svarlist-p vars).

Definitions and Theorems

Function: svtv-override-triple-relevant-vars

(defun svtv-override-triple-relevant-vars (triple spec)
  (declare (xargs :guard (and (svtv-override-triple-p triple)
                              (svex-env-p spec))))
  (let ((__function__ 'svtv-override-triple-relevant-vars))
    (declare (ignorable __function__))
    (b* (((svtv-override-triple triple)))
      (if (equal (svex-eval triple.val spec)
                 (4vec-x))
          (svex-vars triple.test)
        (append (svex-vars triple.test)
                (svex-vars triple.val))))))

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

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

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

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

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

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

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

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

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

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

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

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