 Another kind of substructural approach works by attacking various structural rules associated with transitivity of consequence. The best-known of these rules is the rule of cut, which allows us to move from \(\Gamma \vdash B\) and \(\Delta , B \vdash C\) to \(\Delta , \Gamma \vdash C\). But it can also be worth considering other transitivity-related properties, such as the one called simple transitivity in Weir 2015, proceeding from \(A \vdash B\) and \(B \vdash C\) to \(A \vdash C\). (That is, simple transitivity is the special case of cut where \(\Delta\) is empty and \(\Gamma\) is a singleton.)