  We have measured the superconducting penetration depth~$\Lambda(T)$ in the
heavy-fermion/intermediate-valent superconducting alloy
series~Ce$_{1-x}$Yb$_x$CoIn$_5$ using transverse-field muon spin relaxation, to
study the effect of intermediate-valent Yb doping on Fermi-liquid
renormalization. From $\Lambda(T)$ we determine the superfluid density
$\rho_s(T)$, and find that it decreases continuously with increasing nominal Yb
concentration~$x$, i.e., with increasing intermediate valence. The
temperature-dependent renormalization of the "normal" fluid density~$\rho_N(T)
= \rho_s(0) - \rho_s(T)$ in both the heavy-fermion and intermediate valence
limits is proportional to the temperature-dependent renormalization of the
specific heat. This indicates that the temperature-dependent Fermi-liquid
Landau parameters of the superconducting quasiparticles entering the two
different physical quantities are the same. These results represent an
important advance in understanding of both intermediate valence and
heavy-fermion phenomena in superconductors.
