  The boundary of topological phases of matter can manifest its topology
nature, which leads to the so-called boundary-bulk correspondence (BBC) of
topological phases. In this Letter, we construct a one-to-one correspondence
between the boundary theories of fermionic SPT (fSPT) phases protected by
crystalline symmetry and on-site symmetry in 2D fermionic systems, which follow
the so-called crystalline equivalence principle. We dub such correspondence
crystalline equivalent BBC. We illustrate this correspondence by two simple
examples and as an application, we discover the topological boundary theory of
2D fSPT phase with spin-1/2 fermions, protected by a non-Abelian group
$\mathbb{Z}_4\rtimes\mathbb{Z}_2^T$ with $A^4=\mathcal{T}^2=P_f$ where $A$ is
the generator of $\mathbb{Z}_4$, from its crystalline equivalent partner -- 2D
higher-order fSPT phase with spinless fermions, protected by $D_4$ symmetry.
