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g: z \mapsto \begin{cases}[br]f(z) & z \in X \setminus \{x \cap f^{-1}(y)\} \\[br]f(x) & z = x\\[br]y & z = f^{-1}(y)[br]\end{cases}[br]
g(i) = \begin{cases}[br]f(t) \hspace{14pt} i = x \\[br]f(x) \hspace{11.5pt} i = t \\[br]f(i) \hspace{14pt} i \neq x \wedge i \neq t \\[br]\end{cases}
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