(*+ Final instantiation *)

Record CSL_proof := {
  CSL_prog : Clight.program;
  CSL_CS: compspecs;
  CSL_V : varspecs; 
  CSL_G : funspecs;
  CSL_ext_link : string -> ident;
  CSL_ext_link_inj : forall s1 s2, CSL_ext_link s1 = CSL_ext_link s2 -> s1 = s2;
  CSL_all_safe : semax_prog.semax_prog (Concurrent_Espec unit CSL_CS CSL_ext_link)
                             CSL_prog CSL_V CSL_G;
  CSL_init_mem_not_none : Genv.init_mem CSL_prog <> None;
}.(*+ Final instantiation *)

Record CSL_proof := {
  CSL_prog : Clight.program;
  CSL_CS: compspecs;
  CSL_V : varspecs; 
  CSL_G : funspecs;
  CSL_ext_link : string -> ident;
  CSL_ext_link_inj : forall s1 s2, CSL_ext_link s1 = CSL_ext_link s2 -> s1 = s2;
  CSL_all_safe : semax_prog.semax_prog (Concurrent_Espec unit CSL_CS CSL_ext_link)
                             CSL_prog CSL_V CSL_G;
  CSL_init_mem_not_none : Genv.init_mem CSL_prog <> None;
}.(*+ Final instantiation *)

Record CSL_proof := {
  CSL_prog : Clight.program;
  CSL_CS: compspecs;
  CSL_V : varspecs; 
  CSL_G : funspecs;
  CSL_ext_link : string -> ident;
  CSL_ext_link_inj : forall s1 s2, CSL_ext_link s1 = CSL_ext_link s2 -> s1 = s2;
  CSL_all_safe : semax_prog.semax_prog (Concurrent_Espec unit CSL_CS CSL_ext_link)
                             CSL_prog CSL_V CSL_G;
  CSL_init_mem_not_none : Genv.init_mem CSL_prog <> None;
}.(*+ Final instantiation *)

Record CSL_proof := {
  CSL_prog : Clight.program;
  CSL_CS: compspecs;
  CSL_V : varspecs; 
  CSL_G : funspecs;
  CSL_ext_link : string -> ident;
  CSL_ext_link_inj : forall s1 s2, CSL_ext_link s1 = CSL_ext_link s2 -> s1 = s2;
  CSL_all_safe : semax_prog.semax_prog (Concurrent_Espec unit CSL_CS CSL_ext_link)
                             CSL_prog CSL_V CSL_G;
  CSL_init_mem_not_none : Genv.init_mem CSL_prog <> None;
}.(*+ Final instantiation *)

Record CSL_proof := {
  CSL_prog : Clight.program;
  CSL_CS: compspecs;
  CSL_V : varspecs; 
  CSL_G : funspecs;
  CSL_ext_link : string -> ident;
  CSL_ext_link_inj : forall s1 s2, CSL_ext_link s1 = CSL_ext_link s2 -> s1 = s2;
  CSL_all_safe : semax_prog.semax_prog (Concurrent_Espec unit CSL_CS CSL_ext_link)
                             CSL_prog CSL_V CSL_G;
  CSL_init_mem_not_none : Genv.init_mem CSL_prog <> None;
}.(*+ Final instantiation *)

Record CSL_proof := {
  CSL_prog : Clight.program;
  CSL_CS: compspecs;
  CSL_V : varspecs; 
  CSL_G : funspecs;
  CSL_ext_link : string -> ident;
  CSL_ext_link_inj : forall s1 s2, CSL_ext_link s1 = CSL_ext_link s2 -> s1 = s2;
  CSL_all_safe : semax_prog.semax_prog (Concurrent_Espec unit CSL_CS CSL_ext_link)
                             CSL_prog CSL_V CSL_G;
  CSL_init_mem_not_none : Genv.init_mem CSL_prog <> None;
}.(*+ Final instantiation *)

Record CSL_proof := {
  CSL_prog : Clight.program;
  CSL_CS: compspecs;
  CSL_V : varspecs; 
  CSL_G : funspecs;
  CSL_ext_link : string -> ident;
  CSL_ext_link_inj : forall s1 s2, CSL_ext_link s1 = CSL_ext_link s2 -> s1 = s2;
  CSL_all_safe : semax_prog.semax_prog (Concurrent_Espec unit CSL_CS CSL_ext_link)
                             CSL_prog CSL_V CSL_G;
  CSL_init_mem_not_none : Genv.init_mem CSL_prog <> None;
}.(*+ Final instantiation *)

Record CSL_proof := {
  CSL_prog : Clight.program;
  CSL_CS: compspecs;
  CSL_V : varspecs; 
  CSL_G : funspecs;
  CSL_ext_link : string -> ident;
  CSL_ext_link_inj : forall s1 s2, CSL_ext_link s1 = CSL_ext_link s2 -> s1 = s2;
  CSL_all_safe : semax_prog.semax_prog (Concurrent_Espec unit CSL_CS CSL_ext_link)
                             CSL_prog CSL_V CSL_G;
  CSL_init_mem_not_none : Genv.init_mem CSL_prog <> None;
}.(*+ Final instantiation *)

Record CSL_proof := {
  CSL_prog : Clight.program;
  CSL_CS: compspecs;
  CSL_V : varspecs; 
  CSL_G : funspecs;
  CSL_ext_link : string -> ident;
  CSL_ext_link_inj : forall s1 s2, CSL_ext_link s1 = CSL_ext_link s2 -> s1 = s2;
  CSL_all_safe : semax_prog.semax_prog (Concurrent_Espec unit CSL_CS CSL_ext_link)
                             CSL_prog CSL_V CSL_G;
  CSL_init_mem_not_none : Genv.init_mem CSL_prog <> None;
}.Definition CS :=   CPROOF.(CSL_CS).Definition V :=   CPROOF.(CSL_V).Definition G :=   CPROOF.(CSL_G).Definition ext_link :=   CPROOF.(CSL_ext_link).Definition ext_link_inj :=   CPROOF.(CSL_ext_link_inj).Definition prog :=   CPROOF.(CSL_prog).Definition all_safe :=   CPROOF.(CSL_all_safe).Definition init_mem_not_none :=   CPROOF.(CSL_init_mem_not_none).Definition Jspec' := (@OK_spec (Concurrent_Espec unit CS ext_link)).(* another, looser invariant to have more standard preservation
  statement *)
  Definition inv Gamma n state :=
    exists m, (n <= m)%nat /\ state_invariant(ge := globalenv prog) Jspec' Gamma m state.

Lemma inv_sch_irr Gamma n m i tr sch sch' tp : inv Gamma n (m, (tr, i :: sch, tp)) -> inv Gamma n (m, (tr, i :: sch', tp)).