Inductive match_ctl : ctl -> ctl -> Prop :=
| match_Krun c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Krun c) (Krun c')
| match_Kblocked c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kblocked c) (Kblocked c')
| match_Kresume c c' v : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kresume c v) (Kresume c' v)
| match_Kinit v v' : match_ctl (Kinit v v') (Kinit v v').Inductive match_ctl : ctl -> ctl -> Prop :=
| match_Krun c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Krun c) (Krun c')
| match_Kblocked c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kblocked c) (Kblocked c')
| match_Kresume c c' v : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kresume c v) (Kresume c' v)
| match_Kinit v v' : match_ctl (Kinit v v') (Kinit v v').Inductive match_ctl : ctl -> ctl -> Prop :=
| match_Krun c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Krun c) (Krun c')
| match_Kblocked c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kblocked c) (Kblocked c')
| match_Kresume c c' v : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kresume c v) (Kresume c' v)
| match_Kinit v v' : match_ctl (Kinit v v') (Kinit v v').Inductive match_ctl : ctl -> ctl -> Prop :=
| match_Krun c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Krun c) (Krun c')
| match_Kblocked c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kblocked c) (Kblocked c')
| match_Kresume c c' v : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kresume c v) (Kresume c' v)
| match_Kinit v v' : match_ctl (Kinit v v') (Kinit v v').Inductive match_ctl : ctl -> ctl -> Prop :=
| match_Krun c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Krun c) (Krun c')
| match_Kblocked c c' : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kblocked c) (Kblocked c')
| match_Kresume c c' v : match_states c (fst (CC'.CC_state_to_CC_core c')) -> match_ctl (Kresume c v) (Kresume c' v)
| match_Kinit v v' : match_ctl (Kinit v v') (Kinit v v').

Lemma restrPerm_sub_map: forall m p Hlt, sub_map (snd (getMaxPerm (@restrPermMap p m Hlt))) (snd (getMaxPerm m)).