After introducing the didactic imperative programming language IMP, Nipkow and Klein's book on formal programming language semantics (version of March 2021) specifies compilation of IMP commands into a lower-level language based on a stack machine, and expounds a formal verification of that compiler. Exercise 8.4 asks the reader to adjust such proof for a new compilation target, consisting of a machine language that (i) accesses memory locations through their addresses instead of variable names, and (ii) maintains a stack in memory via a stack pointer rather than relying upon a built-in stack. A natural strategy to maximize reuse of the original proof is keeping the original language as an assembly one and splitting compilation into multiple steps, namely a source-to-assembly step matching the original compilation process followed by an assembly-to-machine step. In this way, proving assembly code-machine code equivalence is the only extant task. A previous paper by the present author introduces a reasoning toolbox that allows for a compiler correctness proof shorter than the book's one, as such promising to constitute a further enhanced reference for the formal verification of real-world compilers. This paper in turn shows that such toolbox can be reused to accomplish the aforesaid task as well, which demonstrates that the proposed approach also promotes proof reuse in multi-stage compiler verifications.