\begin{align}
a \rightarrow b &\implies a = b. \tag{Equal} \\
\text{Let } a = c \text{. } a \rightarrow b \text{, } m(a) &\implies a \not = b \wedge b = c. \tag{Disjoint}
\end{align}
\begin{align}
\text{Let } a = c \text{. } a \rightarrow b \text{, } m(a) &\implies a \not = b \wedge b = c. \tag{Copies are Disjoint}
\end{align}