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The deductive method reduces verification of safety properties of programs to, first, proposing inductive assertions and, second, proving the validity of the resulting set of first-order verification conditions. We discuss the transition from verification conditions to verification constraints that occurs when the deductive method is applied to parameterized assertions instead of fixed expressions (e.g., p0 + p1j + p2k ≥0, for parameters p0, p1, and p2, instead of 3 + j – k ≥0) in order to discover inductive assertions. We then introduce two new verification constraint forms that enable the incremental and property-directed construction of inductive assertions. We describe an iterative method for solving the resulting constraint problems. The main advantage of this approach is that it uses off-the-shelf constraint solvers and thus directly benefits from progress in constraint solving.