We consider the problem of efficiently checking a set of safety properties P 1 , . . . , P k of one design. We introduce a new approach called JA-verification, where JA stands for "Just-Assume" (as opposed to "assume-guarantee"). In this approach, when proving a property P i , one assumes that every property P j for j = i holds. The process of proving properties either results in showing that P 1 , . . . , P k hold without any assumptions or finding a "debugging set" of properties. The latter identifies a subset of failed properties that are the first to break. The design behaviors that cause the properties in the debugging set to fail must be fixed first. Importantly, in our approach, there is no need to prove the assumptions used. We describe the theory behind our approach and report experimental results that demonstrate substantial gains in performance, especially in the cases where a small debugging set exists. * This is an extended version of the paper published at DATE-2018.