Logically: Constrains X to be less than or equal to Y. X and Y are partial linear expressions. Partial linear expressions may contain terms of the form implicit_sum(+Var) in addition to any terms allowed within a standard linear expression. Variables occurring inside implicit_sum/1 terms are taken to be subproblem variables whose instantiation will correspond to the coefficient of a generated master problem variable in this constraint. Operationally, the constraint gets delayed until the external solver state for ColgenInstance is invoked.
The $ version of the arithmetic constraints are provided to allow code to be written which does not specify the solver. They are equivalent to their colgen instance counterparts without the $ prefix.