This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

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v. Simple past tense and past participle of preestablish.

"Rather, their brains come prefitted with an area for absorbing linguistic information—not just absorbing it, but actually sorting the bits of speech they first hear into preestablished categories."

preestablished    preestablishes    preestablishing   

preëstablished harmony