  We present new estimates of redshift-dependent luminosity functions of IR
lines detectable by SPICA/SAFARI and excited both by star formation and by AGN
activity. The new estimates improve over previous work by using updated
evolutionary models and dealing in a self consistent way with emission of
galaxies as a whole, including both the starburst and the AGN component. New
relationships between line and AGN bolometric luminosity have been derived and
those between line and IR luminosities of the starburst component have been
updated. These ingredients were used to work out predictions for the source
counts in 11 mid/far-IR emission lines partially or entirely excited by AGN
activity. We find that the statistics of the emission line detection of
galaxies as a whole is mainly determined by the star formation rate, because of
the rarity of bright AGNs. We also find that the slope of the line integral
number counts is flatter than 2 implying that the number of detections at fixed
observing time increases more by extending the survey area than by going
deeper. We thus propose a wide spectroscopic survey of 1 hour integration per
field-of-view over an area of 5 deg$^{2}$ to detect (at 5$\sigma$) $\sim$760
AGNs in [OIV]25.89$\mu$m $-$ the brightest AGN mid-infrared line $-$ out to
$z\sim2$. Pointed observations of strongly lensed or hyper-luminous galaxies
previously detected by large area surveys such as those by Herschel and by the
SPT can provide key information on the galaxy-AGN co-evolution out to higher
redshifts.
