End explicit_safetyN_stutter.
Section The_Equivalence.
Context (core_data: Type)
(core_ord : core_data -> core_data -> Prop)
(core_ord_wf: well_founded core_ord)
(default: core_data).

Theorem safety_stutter_stepN_equiv:
forall x y,
valid x y ->
exp_safety x y <-> exists cd, @exp_safetyN_stutter _ core_ord cd x y.