  Hybrid systems theorem proving provides strong correctness guarantees about
the interacting discrete and continuous dynamics of cyber-physical systems. The
trustworthiness of proofs rests on the soundness of the proof calculus and its
correct implementation in a theorem prover. Correctness is easier to achieve
with a soundness-critical core that is stripped to the bare minimum, but, as a
consequence, proof convenience has to be regained outside the
soundness-critical core with proof management techniques. We present modeling
and proof management techniques that are built on top of the soundness-critical
core of KeYmaera X to enable expanding definitions, parametric proofs, lemmas,
and other useful proof techniques in hybrid systems proofs. Our techniques
steer the uniform substitution implementation of the differential dynamic logic
proof calculus in KeYmaera X to allow users choose when and how in a proof
abstract formulas, terms, or programs become expanded to their concrete
definitions, and when and how lemmas and sub-proofs are combined to a full
proof. The same techniques are exploited in implicit sub-proofs (without making
such sub-proofs explicit to the user) to provide proof features, such as
temporarily hiding formulas, which are notoriously difficult to get right when
implemented in the prover core, but become trustworthy as proof management
techniques outside the core. We illustrate our approach with several useful
proof techniques and discuss their presentation on the KeYmaera X user
interface.

Logic in Computer Science