It has become fairly standard in the programming-languages research world to verify functional programs in proof assistants using induction, algebraic simplification, and rewriting. In this paper, we introduce Kami, a Coq library that enables similar expressive and modular reasoning for hardware designs expressed in the style of the Bluespec language. We can specify, implement, and verify realistic designs entirely within Coq, ending with automatic extraction into a pipeline that bottoms out in FPGAs. Our methodology, using labeled transition systems, has been evaluated in a case study verifying an infinite family of multicore systems, with cache-coherent shared memory and pipelined cores implementing (the base integer subset of) the RISC-V instruction set.