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provided

On condition; by stipulation; with the understanding; if; usually followed by that; as, provided that nothing in this act shall prejudice the rights of any person whatever. Provided the deductions are logical, they seem almost indifferent to their truth. (G. H. Lewes)

This word is strictly a participle, and the word being is understood, the participle provided agreeing with the whole sentence absolute, and being equivalent to this condition being previously stipulated or established.