A new representation theorem of L-subsets

In the paper, the implication and tensor operations of strong L-nested systems are found, and further we show that the family of all strong L-nested systems on a universal set forms a complete Girard residuated lattice provided the underlying complete residuated lattice is Girard. Finally, an isomorphism of complete Girard residuated lattices between the family of all strong L-nested systems and the L-power set for any fixed universal set is established, and thus a new representation theorem of L-subsets is obtained.