In this paper we aim at extending the non-derivable condensed representation in frequent itemset mining to sequential pattern mining. We start by showing a negative example: in this context of frequent sequences, the notion of non-derivability is meaningless. Therefore, we extend our focus to the mining of conjunctions of sequences. Besides of being of practical importance, this class of patterns has some nice theoretical properties. Based on a new unexploited theoretical definition of equivalence classes for sequential patterns, we are able to extend the notion of a non-derivable itemset to the sequence domain. We present a new depth-first approach to mine non-derivable conjunctive sequential patterns and show its use in mining association rules for sequences. This approach is based on a well-known combinatorial theorem: the Möbius inversion. A performance study using both synthetic and real datasets illustrates the efficiency of our mining algorithm. These new introduced patterns have a high-potential for real-life applications, especially for network monitoring and biomedical fields with the ability to get sequential association rules with all the classical statistical metrics such as confidence, conviction, lift, etc.