Module Partial := ForwardTrace (ProgramState.Partial).Module Total := ForwardTrace (ProgramState.Total).

(* Specifications: *)
Lemma Total2Partial_forward_trace {state: Type} {state_R: Relation state}: Included _ Total.forward_trace Partial.forward_trace.
Lemma Total2Partial_forward_trace_with_test {state: Type} {state_R: Relation state} (P: state -> Prop): Included _ (Total.forward_trace_with_test P) (Partial.forward_trace_with_test P).