Admitted.

Lemma concur_stable_thread_step_target:
forall  cd f (c1:C1) m1 c2 m2 f' ts1' m1' ts2' m2' tid,
forall (Htid1: containsThread c1 tid)
(Htid2: containsThread c2 tid)
(LT : (tid < hb')%nat)
(Hcmpt1: HybridMachine.mem_compatible hb1 Sems Semt c1 m1)
(Hcmpt2: HybridMachine.mem_compatible hb2 Sems Semt c2 m2),
concur_match cd f c1 m1 c2 m2 ->
is_ext f (Mem.nextblock m1) f' (Mem.nextblock m2) ->
semantics.mem_step (restrPermMap (FST (Hcmpt1 _ Htid1))) m1' ->
semantics.mem_step (restrPermMap (FST (Hcmpt2 _ Htid2))) m2' ->
match_self (code_inject Asm_self_simulation) f' ts1' m1' ts2' m2' ->
concur_match cd f'
(updThread Htid1  (Krun (TState _ _ ts1')) (getCurPerm m1', (snd (getThreadR Htid1))))  m1'
(updThread Htid2 (Krun (TState _ _ ts2')) (getCurPerm m2', (snd (getThreadR Htid2)))) m2'.