Inductive InternalOrExternal: MachState -> mem -> MachState -> mem -> Prop:=
| IsInternal st st' m m':
internal_step (fst (fst st)) (snd st) m (snd st') m'  ->
InternalOrExternal st m st' m'
| IsExternal st st' m m':
external_step (fst (fst st)) (snd (fst st)) (snd st) m (fst (fst st')) (snd (fst st')) (snd st') m'  ->
InternalOrExternal st m st' m'.

(* All machine steps are either Internal or External (according to csafe)*)
Lemma step_InternalOrExternal: forall st m st' m',
MachStep st m st' m' ->
InternalOrExternal st m st' m'.