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Given
$$T_m(x,y)=\min(x,y),$$
for all $x,y\in[0,1]$.
Prove $T_m\left(x,T_m(y,z)\right)=T_m(T_m(x,y),z)$.
\begin{align*}
T_m\left(x,T_m(y,z)\right)&=\min(x,T_m(y,z))\\
&=\min(x,\min(y,z))
\end{align*}
Is it right the proof as below?
\begin{align*}
T_m\left(x,T_m(y,z)\right)&=\min(x,y,z)\\
&...