This article is to introduce separable proposition and separable proposition theorem, then to prove theorems in real number field by using separable proposition in a union form.
引入了可分命题和可分命题定理，利用该定理统一证明数学分析中的定理，极大简化了这些定理的证明过程。
The union-representation theorem of both-branch fuzzy set is given, and some operational properties of both-branch fuzzy set are discussed.
建立了双枝模糊集并-表现定理，讨论了双枝模糊集的运算性质。
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