Section UnpackStratifiedSemantics.
Context {W V G S' U F world_erase VU GF}
`{SS : StratifiedSemantics W V G S' U F world_erase VU GF}.

Lemma step_star_erasure : forall w w' s k_w k_w' k_s,
world_erase w = s
-> ctl_erase k_w k_s
-> @step_star _ V G w k_w w' k_w'
-> exists s', exists k_s',
@step_star _ U F s k_s s' k_s'
/\ world_erase w' = s' /\ ctl_erase k_w' k_s'.