Research proof index

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.

If the appended source tree of a SplitData is structured then so is its first-stage tree.

The suffix tree selected by any first-stage path of a structured SplitData is structured.

Lifting the prover intertwines with the process round function