Module Type FORWARD_TRACE.
Declare Module F: FORWARD.
Parameter forward_trace: forall {state: Type} {state_R: Relation state}, traces state.
Parameter forward_trace_with_test: forall {state: Type} {state_R: Relation state} (P: state -> Prop), traces state.

Axiom singleton_trace_forward: forall {state: Type} {state_R: Relation state} s ms,
F.forward (Terminating s) ms ->
forward_trace (singleton_trace s ms).