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We prove in a purely algebraic way that if  L  is an Archimedean truncated vector lattice then there exists a positive element  e  in the universal completion  L uof  L  such that the truncation of  L  is provided by meet with  e . Previous representations of truncated vector lattices by almost-finite extended-real continuous valued functions can be obtained as consequences.

Embedding of a truncated vector lattice into its universal completion