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In this article, we revisit the notion of some hyperbolicity introduced by Pujals and Sambarino [A sufficient condition for robustly minimal foliations. Ergod. Th. & Dynam. Sys. 26(1) (2006), 281–289]. We present a more general definition that, in particular, can be applied to the symplectic context (something that was not possible for the previous one). As an application, we construct 
$C^1$ robustly transitive derived from Anosov diffeomorphisms with mixed behaviour on centre leaves.
