Lift Context process Round

theorem liftContext_processRound    {lens : Context.Lens OuterStmtIn OuterStmtOut InnerStmtIn InnerStmtOut                        OuterWitIn OuterWitOut InnerWitIn InnerWitOut}    {i : Fin n}    {P : Prover oSpec InnerStmtIn InnerWitIn InnerStmtOut InnerWitOut pSpec}    {resultRound : OracleComp (oSpec + [pSpec.Challenge]ₒ)      (pSpec.Transcript i.castSucc × (P.liftContext lens).PrvState i.castSucc)} :      (P.liftContext lens).processRound i resultRound      = do        let ⟨transcript, prvState, outerStmtIn, outerWitIn⟩ ← resultRound        let ⟨newTranscript, newPrvState⟩ ← P.processRound i (do return ⟨transcript, prvState⟩)        return ⟨newTranscript, ⟨newPrvState, outerStmtIn, outerWitIn⟩⟩ := by  unfold processRound liftContext  simp only [bind_pure_comp]  congr 1; funext ⟨tr, ps, outerStmtIn', outerWitIn'⟩  simp only [pure_bind]  split <;> simp [Functor.map_map, Function.comp, liftM_map, map_bind,    bind_assoc, pure_bind, bind_map_left, bind_pure_comp]