Research proof index

The stateful-responder probability bridge: running an adversary against the responder built from a StateT σ ProbComp handler (ofStateQueryImpl impl) is exactly the evaluation distribution of running it against impl itself , the responder's SPMF program-run is 𝒟 of the ProbComp program-run, jointly in the returned value and the final sta...

Recombining a first-stage path with a suffix leaf gives a leaf transcript of the appended tree.

leftPrefix commutes with extending the prefix by one round.

rightPrefix commutes with extending the right prefix by one round. The rightPrefix/Fin.snoc dites are split by split_ifs; contradictory combinations close by omega (with idx's bound), matching ones by cast_eq_cast_of_heq (stripping casts to a base HEq, then rfl/index omega).

At the right boundary (pre₂ is a full right transcript) the embedding is literally tr₁ ++ₜ.

If the appended source tree of a RightProj is structured then so is its right-protocol tree.