CA is trivially satisfied by not being distributed or by tolerating divergence, although the latter case might show how calling it a "theorem" is overselling it: consistency qua "reads receive the most recent writes" can be read as implying partition-tolerance magic. And there are other instances where the simple three-options-pick-two formulation conceals more ambiguities than may be good for it.
You may find Mark Burgess' thoughts on the matter useful.
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