  In this paper, we proposed the GLHUA double layer cloak; proved the
properties of GLHUA double layer cloak; Using GL no scattering inversion and
the pre cloak condition 6.1 to 6.4 in paper [1], we create GLHUA outer layer
cloak radial relative parameter and angular relative parameter theoretically.
We proved theorem 4.1 to theorem 4.4 that the phase velocity of the
electromagnetic wave in GLHUA outer layer cloak is less than light speed and
tends to zero at the boundary $r=R_1$, the EM wave tends to zero at $r=R1$;
When source $r_s > R_2$ in the outside of the cloak and observer $r_o < R_o$ in
the concealment, then $\vec E(\vec r_o)=0$ and $\vec H(\vec r_o)=0$ that is
proved in theorem 5.1 and 5.3. We prove that the EM wave excited in outside of
the cloak can not propagation penetrate into the concealment. In theorem 5.4 to
5.6, we rigorously proved the EM wave excited in outside of the cloak can not
be disturbed by the cloak. In theorem 6.1 to theorem 6.6, we prove that the EM
wave excited in the concealment can not propagate to outside of GLHUA inner
cloak. we prove that the EM wave excited in the concealment can not be
disturbed by the cloak. We theoretically prove that the GLHUA double cloak is
invisible cloak with concealment and with relative parameter not less than 1;
the GLHUA double layer cloak is practicable. In December of 2016, we submitted
3 papers to arXiv for GLHUA double layer cloak with relative parameters not
less than 1. This is the third paper. The task and content of the three paper
are different from each other. The second paper [1] and this Paper are
theoretical base and proof of the subjects in paper arXiv:1612.02857. We find
an exact analytical EM wave field of Maxwell EM equation in GLHUA cloak and
mirage bridge wave. Patent of the GLHUA EM cloaks,GLHUA sphere and GL modeling
and inversion methods are reserved by authors in GL Geophysical Laboratory.
