I know that for an equivalence class $$[a]^{[b]_{\phi(m)}}$$ to be well defined, be must be an equivalence class of $\phi(m)$. However, can we always assume that $$[a]^{[b+c]}= [a]^{[b]_{\phi(m)}}[a]^{[c]_{\phi(m)}}$$ And why is that?
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