End ForwardTrace.
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).