Frequent itemset discovering has been one essential task in data mining. In the worst case, the cardinality of the class of all frequent itemsets is of exponent which leads to many difficulties for users. Therefore, a model of constraintbased mining is necessary when their needs and interests are the top priority. This paper aims to find a structure of frequent itemsets that satisfy the following conditions: they include a subset C 10 , contain no items of a subset C 11 , and have at least an item belonging to subset C 21 . The first new point of the paper is the proposed theoretical result that is the generalization of our former researches (Hai et al. in Adv Comput Methods Knowl Eng Sci 479:367-378, 2013). Second, based on new sufficient and necessary conditions discovered just for closed itemsets and their generators in association with the methods of creating borders and eliminating branches and nodes on the lattice, we can effectively and quickly eliminate not only a class of frequent itemsets but also one or more branches of equivalence classes of which elements are insatiate the constraints. Third, a structure and a unique representation of frequent itemsets with extended double constraints are shown by representative closed itemsets and their generators. Finally, all theoretical results in this paper are proven to be reliable and they are firm bases to guarantee the correctness and efficiency of a new algorithm, MFS-EDC, which is used to effectively mine all constrained frequent itemsets. Experiments show the outstanding efficiency of this