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• Undocumented

Svex-env-keys-equiv

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

Function: svex-env-keys-equiv

(defun svex-env-keys-equiv (x y)
  (and (set-equiv (alist-keys (svex-env-fix x))
                  (alist-keys (svex-env-fix y)))))

Definitions and Theorems

Function: svex-env-keys-equiv

(defun svex-env-keys-equiv (x y)
  (and (set-equiv (alist-keys (svex-env-fix x))
                  (alist-keys (svex-env-fix y)))))

Theorem: svex-env-keys-equiv-is-an-equivalence

(defthm svex-env-keys-equiv-is-an-equivalence
  (and (booleanp (svex-env-keys-equiv x y))
       (svex-env-keys-equiv x x)
       (implies (svex-env-keys-equiv x y)
                (svex-env-keys-equiv y x))
       (implies (and (svex-env-keys-equiv x y)
                     (svex-env-keys-equiv y z))
                (svex-env-keys-equiv x z)))
  :rule-classes (:equivalence))