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All terms describe formal claims that are true. The main difference is in how they are used. A lemma is mathematical claim that is (generally) true. In textbooks, Lemma's are usually either proven, left as an exercise, or assumed to be prior knowledge. A lemma is distinguished from a theorem in that the lemma is usually a less important or intermediate ...


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Its a standard notation in mathematics, called the set-builder notation. Basically, it means: "the set of all $(m,i)$ such that $(m,j)\in T$".


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