  We present the first observational infrared luminosity function (IRLF)
measurement in the Epoch of Reionization (EoR) based on a UV-selected galaxy
sample with ALMA spectroscopic observations. Our analysis is based on the ALMA
large program Reionization Era Bright Emission Line Survey (REBELS), which
targets 42 galaxies at $\mathrm{z=6.4-7.7}$ with [CII] 158$\micron$ line scans.
16 sources exhibit a dust detection, 15 of which are also spectroscopically
confirmed through the [CII] line. The IR luminosities of the sample range from
$\log L_{IR}/L_\odot=11.4$ to 12.2. Using the UVLF as a proxy to derive the
effective volume for each of our target sources, we derive IRLF estimates, both
for detections and for the full sample including IR luminosity upper limits.
The resulting IRLFs are well reproduced by a Schechter function with the
characteristic luminosity of $\log L_{*}/L_\odot=11.6^{+0.2}_{-0.1}$. Our
observational results are in broad agreement with the average of predicted
IRLFs from simulations at $z\sim7$. Conversely, our IRLFs lie significantly
below lower redshift estimates, suggesting a rapid evolution from $z\sim4$ to
$z\sim7$, into the reionization epoch. The inferred obscured contribution to
the cosmic star-formation rate density at $z\sim7$ amounts to
$\mathrm{log(SFRD/M_{\odot}/yr/Mpc^{3}) = -2.66^{+0.17}_{-0.14} }$ which is at
least $\sim$10\% of UV-based estimates. We conclude that the presence of dust
is already abundant in the EoR and discuss the possibility of unveiling larger
samples of dusty galaxies with future ALMA and JWST observations.
