Testing deca - TeV unified compositeness at the 4-TeV mu+ mu- collider

In the framework of the unified compositeness of leptons, quarks and Higgs bosons, the hidden local symmetry \hat H_{loc}= SU(2)_L\times U(1)_Y with the heavy composite vector bosons, in addition to the SM gauge bosons, is briefly described. Supplementary hypothesis of the vector boson dominance (VBD) of the SM gauge interactions is considered. It is argued that this should produce the universal dominant residual interactions of the SM composite particles, i.e., all of the fermions and Higgs bosons. Restrictions on the universal residual fermion-fermion, fermion-boson and boson-boson interactions due to the VBD are investigated. Manifestations of the residual interactions at the 4 TeV mu+mu- collider are studied. It is shown that at 95% C.L. the unified substructure could be investigated at the collider in the processes mu+mu- \to \bar ff up to the compositeness scale O(150 TeV), in the processes mu+mu- \to ZH, W+W- up to O(100 TeV) and in the process mu+mu- \to ZHH up to O(40 TeV), which lie in the naturally preferable Deca-TeV region.