I am not sure if you mean inversing the first function. If you use Cantor–Bernstein–Schroeder theorem, you don't have to construct a bijection (which has to have an inverse). You just have to provide two injections: one from to and one back.when you inverse it...

Well, that should be easy. You can use linear functions for some to map inside , say, into , and into, say, . So, use make two linear functions and then glue them into one using a declaration like if ..., and if ... .

Conversely, you can inject into, say, .