Formal verification in computer science often takes a worst-case view towards performance and uses induction to prove specification invariants. In control theory, robust control takes a worst-case view towards performance; nominal performance proofs often use derivative information to prove invariance of specification sets. In this note, we explore a toolbox for proving (positive) invariance of state-space sets with respect to the actions of dynamical systems. The focus is on dynamical systems given by differential equations, building up to hybrid systems.