We formulate a sound and complete assume-guarantee framework for reasoning compositionally about safety properties of component behaviours. The specification of a component, which constrains the temporal ordering of input and output interactions with the environment, is expressed in terms of two prefix-closed sets of traces: an assumption and guarantee. The framework supports dynamic reasoning about components and specifications, and includes rules for parallel composition, logical conjunction corresponding to independent development, and quotient for incremental synthesis. Practical applicability of the framework is demonstrated by considering a simple printing example.