To improve performance, modern multiprocessors and pro- gramming languages typically implement relaxed memory models that do not require all processors/threads to observe memory operations in the same order. To relieve programmers from having to reason directly about these relaxed behaviors, languages often provide efficient synchro- nization primitives and concurrent data structures with stronger high- level guarantees about memory reorderings. For instance, locks usually ensure that when a thread acquires a lock, it can observe all memory operations of the releasing thread, prior to the release. When used cor- rectly, these synchronization primitives and data structures allow clients to recover a fiction of a sequentially consistent memory model. In this paper we propose a new proof system, iCAP-TSO, that captures this fiction formally, for a language with a TSO memory model. The logic supports reasoning about libraries that directly exploit the relaxed memory model to achieve maximum efficiency. When these libraries pro- vide sufficient guarantees, the logic hides the underlying complexity and admits standard separation logic rules for reasoning about their more high-level clients.