Engineering a product-line is more than just describing a product-line: to be correct, every variant that can be generated must satisfy some constraints. To ensure that all such variants will be correct (e.g. well-typed) there are only two ways: either to check the variants of interest individually or to come up with a complex product-line analysis algorithm, specific to every constraint. In this paper, we address a generalization of this problem: we propose a mechanism that allows to check whether a constraint holds simultaneously for all variants which might be generated. The contribution of this paper is a function that assumes constraints that shall be fulfilled by all variants and generates ("lifts") out of them constraints for the product-line. These lifted constraints can then be checked directly on a model product-line, thus simultaneously be verified for all variants. The lifting is formulated in a very general manner, which allows to make use of generic algorithms like SMT solving or theorem proving in a modular way. We show how to verify lifted constraints using SMT solving by automatically translating model product-lines and constraints. The scalability of the approach is demonstrated with an industrial case study, in which we apply our lifting to a domain specific modeling language of the manufacturing domain.