3.2.4 Definitions Section
In the definitions section, when we want definition extension and expansion possible, we write file names of articles that have their definitions. For instance, when demonstrating X c= Y, we just need to demonstrate ∀a(a in X implies a in Y); however, this definition is defined in the article
TARSKI as below.
pred X c= Y means x in X implies x in Y;
Therefore, if we write TARSKI in the definitions section, when we demonstrate X c= Y, it means that we demonstrated X c= Y if we can say that a in X implies a in Y.
theorem X c=X \/ Y
proof let x be set;
assume x in X;
hence y in X \/ Y by BOOLE:def 2;