Is the mathematical shorthand for the phrase "has the property..." or "satisfies the condition..."? As in, when you have a set of properties or conditions predefined, how can you write that an object has those properties or satisfies those conditions?
For example, in Rudin's Principles of Mathematical Analysis, in the Appendix to "The Real and Complex Number Systems," Rudin defines three properties, (I), (II), and (III) that define a cut. Later on, he tries to prove that various sets satisfy these conditions and are therefore cuts. In Step 3, for instance, he defines a set $\gamma$, then proves that this set satisfies (I), (II), and (III) and is therefore a cut. Is there any symbolic notation for "$\gamma$ satisfies (I)" ?