(** *** Lemmas about invariants preserved by coresteps*)

(** [mem_compatible] is preserved by [initial_core]*)
Lemma initial_core_compatible:
forall (tp : t)  (m m' : mem) i n vf arg
(pf : containsThread tp i) (c: semC)
(Hinv: invariant tp)
(Hcompatible : mem_compatible tp m)
(Hinitial: initial_core semSem n (restrPermMap (DryHybridMachine.compat_th _ _ Hcompatible pf).1) c m' vf arg),
mem_compatible (updThread pf (Krun c) (getCurPerm m', (getThreadR pf).2)) m'.