  The REX (Radio-Emitting X-ray sources) is a catalogue produced by
cross-matching X-ray data from the ROSAT-PSPC archive of pointed observations
and radio data from the NRAO VLA Sky Survey, aimed at the selection of blazars.
From the REX catalogue, we select a well defined and statistically complete
sample of high-energy peaked BL Lac (HBL). HBL are expected to be the most
numerous class of extragalactic TeV emitting sources. Specifically, we have
considered only the REX sources in the currently planned CTA extragalactic
survey area satisfying specific criteria and with an optical spectroscopic
confirmation. We obtain 46 HBL candidates that we called Te-REX (TeV-emitting
REX). We estimate the very high-energy gamma-ray emission, in the TeV domain,
using an empirical approach i.e. using specific statistical relations between
gamma-rays (at GeV energies) and radio/X-rays properties observed in bright HBL
from the literature. We compare the spectral energy distributions (SEDs) with
the sensitivities of current and upcoming Cherenkov telescopes and we predict
that 14 Te-REX could be detectable with 50 hours of observations of CTA and 7
of them also with current Cherenkov facilities in 50 hours. By extrapolating
these numbers on the total extragalactic sky, we predict that about 800 HBL
could be visible in pointed CTA observations and about 400 with current
Cherenkov telescopes in 50 hours. Interestingly, our predictions show that a
non-negligible fraction (about 30%) of the HBL that will be detectable by CTA
is composed of relatively weak objects whose optical nuclear emission is
swamped by the host-galaxy light and not (yet) detected by Fermi-LAT.
