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Undocumented

Svex-envlists-equivalent

This is a universal equivalence, introduced using def-universal-equiv.

Function: svex-envlists-equivalent

(defun svex-envlists-equivalent (x y)
  (declare (xargs :non-executable t))
  (declare (xargs :guard t))
  (declare (xargs :non-executable t))
  (prog2$ (acl2::throw-nonexec-error 'svex-envlists-equivalent
                                     (list x y))
          (let ((n (svex-envlists-equivalent-witness x y)))
            (and (svex-envs-equivalent (nth n x)
                                       (nth n y))
                 (equal (len x) (len y))))))

Definitions and Theorems

Theorem: svex-envlists-equivalent-necc

(defthm svex-envlists-equivalent-necc
  (implies (not (and (svex-envs-equivalent (nth n x)
                                           (nth n y))
                     (equal (len x) (len y))))
           (not (svex-envlists-equivalent x y))))

Theorem: svex-envlists-equivalent-witnessing-witness-rule-correct

(defthm svex-envlists-equivalent-witnessing-witness-rule-correct
  (implies (not ((lambda (n y x)
                   (not (if (svex-envs-equivalent (nth n x)
                                                  (nth n y))
                            (equal (len x) (len y))
                          'nil)))
                 (svex-envlists-equivalent-witness x y)
                 y x))
           (svex-envlists-equivalent x y))
  :rule-classes nil)

Theorem: svex-envlists-equivalent-instancing-instance-rule-correct

(defthm svex-envlists-equivalent-instancing-instance-rule-correct
  (implies (not (if (svex-envs-equivalent (nth n x)
                                          (nth n y))
                    (equal (len x) (len y))
                  'nil))
           (not (svex-envlists-equivalent x y)))
  :rule-classes nil)

Theorem: svex-envlists-equivalent-is-an-equivalence

(defthm svex-envlists-equivalent-is-an-equivalence
  (and (booleanp (svex-envlists-equivalent x y))
       (svex-envlists-equivalent x x)
       (implies (svex-envlists-equivalent x y)
                (svex-envlists-equivalent y x))
       (implies (and (svex-envlists-equivalent x y)
                     (svex-envlists-equivalent y z))
                (svex-envlists-equivalent x z)))
  :rule-classes (:equivalence))