Whichever version we will end up using (relation vs function) we'll need some dynamics preservation:
e.g.:
forall M N w,
L_to_Hyb_term w M N ->
forall M',
step_L (M, w) (M', w) ->
value_Hyb N \/
exists N', step_Hyb (N, w) (N', w) /\ L_to_Hyb_term w M' N'.
Whichever version we will end up using (relation vs function) we'll need some dynamics preservation: e.g.: forall M N w, L_to_Hyb_term w M N -> forall M', step_L (M, w) (M', w) -> value_Hyb N \/ exists N', step_Hyb (N, w) (N', w) /\ L_to_Hyb_term w M' N'.