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order defined by the meet in the universal algebra approach coincides with the original partial order.

Conversely, if is a meet-semilattice, and the partial order is defined as in the universal algebra approach, and for some elements then is the greatest lower bound of with respect to since

and therefore Similarly, and if is another lower bound of then whence

Thus, there is a meet defined by the partial order defined by the original meet, and the two meets coincide.

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