(*Lenb -- meminj_preserves_globales is new, and needed since this property is now
    required by the simulation realtions, rather than only at/efterexternal clauses*)
Inductive match_cores: core_data -> meminj -> CSharpMin_core -> mem -> CMin_core -> mem -> Prop :=
  | MC_states:
      forall d fn s k e le m tfn ts tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s = OK ts)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk  cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn s k e le) m
                   (CMin_State tfn ts tk (Vptr sp Int.zero) te) tm
  | MC_state_seq:
      forall d fn s1 s2 k e le m tfn ts1 tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s1 = OK ts1)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont (Csharpminor.Kseq s2 k) tk cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn (Csharpminor.Sseq s1 s2) k e le) m
                   (CMin_State tfn ts1 tk (Vptr sp Int.zero) te) tm
  | MC_callstate:
      forall d fd args k m tfd targs tk tm j cs cenv
      (TR: transl_fundef fd = OK tfd)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (ISCC: Csharpminor.is_call_cont k)
      (ARGSINJ: val_list_inject j args targs)
      (PG: meminj_preserves_globals ge j),

      match_cores d j (CSharpMin_Callstate fd args k) m
                   (CMin_Callstate tfd targs tk) tm
  | MC_returnstate:
      forall d v k m tv tk tm j cs cenv
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (RESINJ: val_inject j v tv)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_Returnstate v k) m
                   (CMin_Returnstate tv tk) tm.(*Lenb -- meminj_preserves_globales is new, and needed since this property is now
    required by the simulation realtions, rather than only at/efterexternal clauses*)
Inductive match_cores: core_data -> meminj -> CSharpMin_core -> mem -> CMin_core -> mem -> Prop :=
  | MC_states:
      forall d fn s k e le m tfn ts tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s = OK ts)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk  cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn s k e le) m
                   (CMin_State tfn ts tk (Vptr sp Int.zero) te) tm
  | MC_state_seq:
      forall d fn s1 s2 k e le m tfn ts1 tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s1 = OK ts1)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont (Csharpminor.Kseq s2 k) tk cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn (Csharpminor.Sseq s1 s2) k e le) m
                   (CMin_State tfn ts1 tk (Vptr sp Int.zero) te) tm
  | MC_callstate:
      forall d fd args k m tfd targs tk tm j cs cenv
      (TR: transl_fundef fd = OK tfd)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (ISCC: Csharpminor.is_call_cont k)
      (ARGSINJ: val_list_inject j args targs)
      (PG: meminj_preserves_globals ge j),

      match_cores d j (CSharpMin_Callstate fd args k) m
                   (CMin_Callstate tfd targs tk) tm
  | MC_returnstate:
      forall d v k m tv tk tm j cs cenv
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (RESINJ: val_inject j v tv)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_Returnstate v k) m
                   (CMin_Returnstate tv tk) tm.(*Lenb -- meminj_preserves_globales is new, and needed since this property is now
    required by the simulation realtions, rather than only at/efterexternal clauses*)
Inductive match_cores: core_data -> meminj -> CSharpMin_core -> mem -> CMin_core -> mem -> Prop :=
  | MC_states:
      forall d fn s k e le m tfn ts tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s = OK ts)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk  cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn s k e le) m
                   (CMin_State tfn ts tk (Vptr sp Int.zero) te) tm
  | MC_state_seq:
      forall d fn s1 s2 k e le m tfn ts1 tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s1 = OK ts1)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont (Csharpminor.Kseq s2 k) tk cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn (Csharpminor.Sseq s1 s2) k e le) m
                   (CMin_State tfn ts1 tk (Vptr sp Int.zero) te) tm
  | MC_callstate:
      forall d fd args k m tfd targs tk tm j cs cenv
      (TR: transl_fundef fd = OK tfd)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (ISCC: Csharpminor.is_call_cont k)
      (ARGSINJ: val_list_inject j args targs)
      (PG: meminj_preserves_globals ge j),

      match_cores d j (CSharpMin_Callstate fd args k) m
                   (CMin_Callstate tfd targs tk) tm
  | MC_returnstate:
      forall d v k m tv tk tm j cs cenv
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (RESINJ: val_inject j v tv)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_Returnstate v k) m
                   (CMin_Returnstate tv tk) tm.(*Lenb -- meminj_preserves_globales is new, and needed since this property is now
    required by the simulation realtions, rather than only at/efterexternal clauses*)
Inductive match_cores: core_data -> meminj -> CSharpMin_core -> mem -> CMin_core -> mem -> Prop :=
  | MC_states:
      forall d fn s k e le m tfn ts tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s = OK ts)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk  cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn s k e le) m
                   (CMin_State tfn ts tk (Vptr sp Int.zero) te) tm
  | MC_state_seq:
      forall d fn s1 s2 k e le m tfn ts1 tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s1 = OK ts1)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont (Csharpminor.Kseq s2 k) tk cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn (Csharpminor.Sseq s1 s2) k e le) m
                   (CMin_State tfn ts1 tk (Vptr sp Int.zero) te) tm
  | MC_callstate:
      forall d fd args k m tfd targs tk tm j cs cenv
      (TR: transl_fundef fd = OK tfd)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (ISCC: Csharpminor.is_call_cont k)
      (ARGSINJ: val_list_inject j args targs)
      (PG: meminj_preserves_globals ge j),

      match_cores d j (CSharpMin_Callstate fd args k) m
                   (CMin_Callstate tfd targs tk) tm
  | MC_returnstate:
      forall d v k m tv tk tm j cs cenv
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (RESINJ: val_inject j v tv)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_Returnstate v k) m
                   (CMin_Returnstate tv tk) tm.(*Lenb -- meminj_preserves_globales is new, and needed since this property is now
    required by the simulation realtions, rather than only at/efterexternal clauses*)
Inductive match_cores: core_data -> meminj -> CSharpMin_core -> mem -> CMin_core -> mem -> Prop :=
  | MC_states:
      forall d fn s k e le m tfn ts tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s = OK ts)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk  cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn s k e le) m
                   (CMin_State tfn ts tk (Vptr sp Int.zero) te) tm
  | MC_state_seq:
      forall d fn s1 s2 k e le m tfn ts1 tk sp te tm cenv xenv j lo hi cs sz
      (TRF: transl_funbody cenv sz fn = OK tfn)
      (TR: transl_stmt cenv xenv s1 = OK ts1)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm
               (Frame cenv tfn e le te sp lo hi :: cs)
               (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont (Csharpminor.Kseq s2 k) tk cenv xenv cs)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_State fn (Csharpminor.Sseq s1 s2) k e le) m
                   (CMin_State tfn ts1 tk (Vptr sp Int.zero) te) tm
  | MC_callstate:
      forall d fd args k m tfd targs tk tm j cs cenv
      (TR: transl_fundef fd = OK tfd)
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (ISCC: Csharpminor.is_call_cont k)
      (ARGSINJ: val_list_inject j args targs)
      (PG: meminj_preserves_globals ge j),

      match_cores d j (CSharpMin_Callstate fd args k) m
                   (CMin_Callstate tfd targs tk) tm
  | MC_returnstate:
      forall d v k m tv tk tm j cs cenv
      (MINJ: Mem.inject j m tm)
      (MCS: match_callstack prog j m tm cs (Mem.nextblock m) (Mem.nextblock tm))
      (MK: match_cont k tk cenv nil cs)
      (RESINJ: val_inject j v tv)
      (PG: meminj_preserves_globals ge j),
      match_cores d j (CSharpMin_Returnstate v k) m
                   (CMin_Returnstate tv tk) tm.

Lemma MC_after_external:forall (d : core_data) (j j' : meminj) (st1 : core_data) (st2 : CMin_core) (m1 : mem) (e : external_function) (vals1 : list val) (ret1 : val) (m1' m2 m2' : mem) (ret2 : val) (sig : signature), d = st1 /\ match_cores d j st1 m1 st2 m2 -> at_external CSharpMin_core_sem st1 = Some (e, sig, vals1) -> Events.meminj_preserves_globals ge j -> inject_incr j j' -> Events.inject_separated j j' m1 m2 -> Mem.inject j' m1' m2' -> val_inject j' ret1 ret2 -> mem_forward m1 m1' -> Mem.unchanged_on (Events.loc_unmapped j) m1 m1' -> mem_forward m2 m2' -> Mem.unchanged_on (Events.loc_out_of_reach j m1) m2 m2' -> exists st1' : core_data, exists st2' : CMin_core, exists d' : core_data, after_external CSharpMin_core_sem (Some ret1) st1 = Some st1' /\ after_external CMin_core_sem (Some ret2) st2 = Some st2' /\ d' = st1' /\ match_cores d' j' st1' m1' st2' m2'.