  We recall some abstract connectivity concepts, and apply them to special
chains in partially ordered sets, called veins, that are defined as
order-convex chains that are contained in every maximal chain they meet. Veins
enable us to define a new partial order on the same underlying set, called the
pruning order. The associated pruned poset is simpler than the initial poset,
but irreducible, coirreducible, and doubly-irreducible elements are preserved
by the operation of pruning.
