This is trivial: If there is a transitive FRG subgraph of G whose sum of edges ≥ α, then choosing the same edges will yield a transitive FRG subgraph of G whose sum of edges ≥ α.
the first rule was annotated in the rule application Others seek medical care ⇒ Others apply for medical care (Recall that crowdsourcing was used to annotate rule applications, and rules were extracted from these applications.)