The TLA+ Proof System (TLAPS) mechanically checks TLA+ proofs. TLA+ is a general-purpose formal specification language that is particularly useful for describing concurrent and distributed systems. The TLA+ proof language is declarative, hierarchical, and scalable to large system specifications. It provides a consistent abstraction over the various “backend” verifiers. The current release of TLAPS does not perform temporal reasoning, and it does not handle some features of TLA+. See the list of currently unsupported TLA+ features. An extension to the full TLA+ language is under active development. However, TLAPS is now suitable for verifying safety properties of non-trivial algorithms. (Only trivial temporal-logic reasoning that is easily checked by hand is needed for safety.) For examples, see the proof of a Byzantine Paxos algorithm and the proof of a security architecture.