  In this paper, we provide an alternative appraoch to an expectaion of
F\"assler et al [J. Geom. Anal. 2016] by showing that a metrically quasiregular
mapping between two equiregular subRiemannian manifolds of homogeneous
dimension $Q\geq 2$ has a negligible branch set. One main new ingredient is to
develop a suitable extension of the generalized Pansu differentiability theory,
in spirit of earlier works by Margulis-Mostow, Karmanova and Vodopyanov.
Another new ingredient is to apply the theory of Sobolev spaces based on upper
gradients developed by Heinonen, Koskela, Shanmugalingam and Tyson to establish
the necessary analytic foundations.
