Suppose $x_{1},x_{2}, \cdots ,x_{n}$ are binaries.
I would like to model the following:
IF $x_{1} + x_{2}+ \cdots +x_{n} \ge 2$ THEN $x_{1} + x_{2} = 2$
IF $x_{1} + x_{2}+ \cdots +x_{n} \ge 3$ THEN $x_{1} + x_{2} + x_{3}= 3$
and so on.
Is there a better way than asking for the following
$(x_{1} \ge 1) \lor (x_{1} + x_{2} \ge 2) \lor (x_{1} + x_{2} + x_{3} \ge 3) \cdots $, which then requires the introduction of additional binaries?