Ah, here’s the diagrammatic version of Lemma 2 that actually seems right: We have Ω ← L → Ω and X_i ← L → X_ibar so by dangly bits X_i ← L (-> Ω) → X_ibar then since you can reroot trees we have Ω → L (-> X_i) → X_ibar, then marginalize out L to get the mediation.
Ah, here’s the diagrammatic version of Lemma 2 that actually seems right: We have Ω ← L → Ω and X_i ← L → X_ibar so by dangly bits X_i ← L (-> Ω) → X_ibar then since you can reroot trees we have Ω → L (-> X_i) → X_ibar, then marginalize out L to get the mediation.