The compact theorem is proved, which states that theory T has model if and only if any finitesubset of T has model.
利用中介逻辑的完备性，本文证明了紧致性定理，即一理论有模型当且仅当其任一有穷子集有模型。
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And finally we prove that let a be a subset of real Numbers, if every continuous function which is defined on a and taken value in a has fixed point, then a is a finite closed interval.
Absrtact: the problem of repetitive computing exits in the process of transition from non-deterministic finite automata to deterministic finite automata using the subset construction method.