(** ** Relating stacks *)

Inductive match_stacks (F: meminj) (m m': mem):
             list stackframe -> list stackframe -> block -> Prop :=
  | match_stacks_nil: forall bound1 bound
        (MG: match_globalenvs F bound1)
        (BELOW: Ple bound1 bound),
      match_stacks F m m' nil nil bound
  | match_stacks_cons: forall res f sp pc rs stk f' sp' rs' stk' bound fenv ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx f f'.(fn_code))
        (AG: agree_regs F ctx rs rs')
        (SP: F sp = Some(sp', ctx.(dstk)))
        (PRIV: range_private F m m' sp' (ctx.(dstk) + ctx.(mstk)) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RES: Ple res ctx.(mreg))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                   (Stackframe (sreg ctx res) f' (Vptr sp' Ptrofs.zero) (spc ctx pc) rs' :: stk')
                   bound
  | match_stacks_untailcall: forall stk res f' sp' rpc rs' stk' bound ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (PRIV: range_private F m m' sp' ctx.(dstk) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RET: ctx.(retinfo) = Some (rpc, res))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   stk
                   (Stackframe res f' (Vptr sp' Ptrofs.zero) rpc rs' :: stk')
                   bound

with match_stacks_inside (F: meminj) (m m': mem):
        list stackframe -> list stackframe -> function -> context -> block -> regset -> Prop :=
  | match_stacks_inside_base: forall stk stk' f' ctx sp' rs'
        (MS: match_stacks F m m' stk stk' sp')
        (RET: ctx.(retinfo) = None)
        (DSTK: ctx.(dstk) = 0),
      match_stacks_inside F m m' stk stk' f' ctx sp' rs'
  | match_stacks_inside_inlined: forall res f sp pc rs stk stk' f' fenv ctx sp' rs' ctx'
        (MS: match_stacks_inside F m m' stk stk' f' ctx' sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx' f f'.(fn_code))
        (AG: agree_regs F ctx' rs rs')
        (SP: F sp = Some(sp', ctx'.(dstk)))
        (PAD: range_private F m m' sp' (ctx'.(dstk) + ctx'.(mstk)) ctx.(dstk))
        (RES: Ple res ctx'.(mreg))
        (RET: ctx.(retinfo) = Some (spc ctx' pc, sreg ctx' res))
        (BELOW: context_below ctx' ctx)
        (SBELOW: context_stack_call ctx' ctx),
      match_stacks_inside F m m' (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                                 stk' f' ctx sp' rs'.(** ** Relating stacks *)

Inductive match_stacks (F: meminj) (m m': mem):
             list stackframe -> list stackframe -> block -> Prop :=
  | match_stacks_nil: forall bound1 bound
        (MG: match_globalenvs F bound1)
        (BELOW: Ple bound1 bound),
      match_stacks F m m' nil nil bound
  | match_stacks_cons: forall res f sp pc rs stk f' sp' rs' stk' bound fenv ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx f f'.(fn_code))
        (AG: agree_regs F ctx rs rs')
        (SP: F sp = Some(sp', ctx.(dstk)))
        (PRIV: range_private F m m' sp' (ctx.(dstk) + ctx.(mstk)) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RES: Ple res ctx.(mreg))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                   (Stackframe (sreg ctx res) f' (Vptr sp' Ptrofs.zero) (spc ctx pc) rs' :: stk')
                   bound
  | match_stacks_untailcall: forall stk res f' sp' rpc rs' stk' bound ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (PRIV: range_private F m m' sp' ctx.(dstk) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RET: ctx.(retinfo) = Some (rpc, res))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   stk
                   (Stackframe res f' (Vptr sp' Ptrofs.zero) rpc rs' :: stk')
                   bound

with match_stacks_inside (F: meminj) (m m': mem):
        list stackframe -> list stackframe -> function -> context -> block -> regset -> Prop :=
  | match_stacks_inside_base: forall stk stk' f' ctx sp' rs'
        (MS: match_stacks F m m' stk stk' sp')
        (RET: ctx.(retinfo) = None)
        (DSTK: ctx.(dstk) = 0),
      match_stacks_inside F m m' stk stk' f' ctx sp' rs'
  | match_stacks_inside_inlined: forall res f sp pc rs stk stk' f' fenv ctx sp' rs' ctx'
        (MS: match_stacks_inside F m m' stk stk' f' ctx' sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx' f f'.(fn_code))
        (AG: agree_regs F ctx' rs rs')
        (SP: F sp = Some(sp', ctx'.(dstk)))
        (PAD: range_private F m m' sp' (ctx'.(dstk) + ctx'.(mstk)) ctx.(dstk))
        (RES: Ple res ctx'.(mreg))
        (RET: ctx.(retinfo) = Some (spc ctx' pc, sreg ctx' res))
        (BELOW: context_below ctx' ctx)
        (SBELOW: context_stack_call ctx' ctx),
      match_stacks_inside F m m' (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                                 stk' f' ctx sp' rs'.(** ** Relating stacks *)

Inductive match_stacks (F: meminj) (m m': mem):
             list stackframe -> list stackframe -> block -> Prop :=
  | match_stacks_nil: forall bound1 bound
        (MG: match_globalenvs F bound1)
        (BELOW: Ple bound1 bound),
      match_stacks F m m' nil nil bound
  | match_stacks_cons: forall res f sp pc rs stk f' sp' rs' stk' bound fenv ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx f f'.(fn_code))
        (AG: agree_regs F ctx rs rs')
        (SP: F sp = Some(sp', ctx.(dstk)))
        (PRIV: range_private F m m' sp' (ctx.(dstk) + ctx.(mstk)) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RES: Ple res ctx.(mreg))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                   (Stackframe (sreg ctx res) f' (Vptr sp' Ptrofs.zero) (spc ctx pc) rs' :: stk')
                   bound
  | match_stacks_untailcall: forall stk res f' sp' rpc rs' stk' bound ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (PRIV: range_private F m m' sp' ctx.(dstk) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RET: ctx.(retinfo) = Some (rpc, res))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   stk
                   (Stackframe res f' (Vptr sp' Ptrofs.zero) rpc rs' :: stk')
                   bound

with match_stacks_inside (F: meminj) (m m': mem):
        list stackframe -> list stackframe -> function -> context -> block -> regset -> Prop :=
  | match_stacks_inside_base: forall stk stk' f' ctx sp' rs'
        (MS: match_stacks F m m' stk stk' sp')
        (RET: ctx.(retinfo) = None)
        (DSTK: ctx.(dstk) = 0),
      match_stacks_inside F m m' stk stk' f' ctx sp' rs'
  | match_stacks_inside_inlined: forall res f sp pc rs stk stk' f' fenv ctx sp' rs' ctx'
        (MS: match_stacks_inside F m m' stk stk' f' ctx' sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx' f f'.(fn_code))
        (AG: agree_regs F ctx' rs rs')
        (SP: F sp = Some(sp', ctx'.(dstk)))
        (PAD: range_private F m m' sp' (ctx'.(dstk) + ctx'.(mstk)) ctx.(dstk))
        (RES: Ple res ctx'.(mreg))
        (RET: ctx.(retinfo) = Some (spc ctx' pc, sreg ctx' res))
        (BELOW: context_below ctx' ctx)
        (SBELOW: context_stack_call ctx' ctx),
      match_stacks_inside F m m' (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                                 stk' f' ctx sp' rs'.(** ** Relating stacks *)

Inductive match_stacks (F: meminj) (m m': mem):
             list stackframe -> list stackframe -> block -> Prop :=
  | match_stacks_nil: forall bound1 bound
        (MG: match_globalenvs F bound1)
        (BELOW: Ple bound1 bound),
      match_stacks F m m' nil nil bound
  | match_stacks_cons: forall res f sp pc rs stk f' sp' rs' stk' bound fenv ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx f f'.(fn_code))
        (AG: agree_regs F ctx rs rs')
        (SP: F sp = Some(sp', ctx.(dstk)))
        (PRIV: range_private F m m' sp' (ctx.(dstk) + ctx.(mstk)) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RES: Ple res ctx.(mreg))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                   (Stackframe (sreg ctx res) f' (Vptr sp' Ptrofs.zero) (spc ctx pc) rs' :: stk')
                   bound
  | match_stacks_untailcall: forall stk res f' sp' rpc rs' stk' bound ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (PRIV: range_private F m m' sp' ctx.(dstk) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RET: ctx.(retinfo) = Some (rpc, res))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   stk
                   (Stackframe res f' (Vptr sp' Ptrofs.zero) rpc rs' :: stk')
                   bound

with match_stacks_inside (F: meminj) (m m': mem):
        list stackframe -> list stackframe -> function -> context -> block -> regset -> Prop :=
  | match_stacks_inside_base: forall stk stk' f' ctx sp' rs'
        (MS: match_stacks F m m' stk stk' sp')
        (RET: ctx.(retinfo) = None)
        (DSTK: ctx.(dstk) = 0),
      match_stacks_inside F m m' stk stk' f' ctx sp' rs'
  | match_stacks_inside_inlined: forall res f sp pc rs stk stk' f' fenv ctx sp' rs' ctx'
        (MS: match_stacks_inside F m m' stk stk' f' ctx' sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx' f f'.(fn_code))
        (AG: agree_regs F ctx' rs rs')
        (SP: F sp = Some(sp', ctx'.(dstk)))
        (PAD: range_private F m m' sp' (ctx'.(dstk) + ctx'.(mstk)) ctx.(dstk))
        (RES: Ple res ctx'.(mreg))
        (RET: ctx.(retinfo) = Some (spc ctx' pc, sreg ctx' res))
        (BELOW: context_below ctx' ctx)
        (SBELOW: context_stack_call ctx' ctx),
      match_stacks_inside F m m' (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                                 stk' f' ctx sp' rs'.(** ** Relating stacks *)

Inductive match_stacks (F: meminj) (m m': mem):
             list stackframe -> list stackframe -> block -> Prop :=
  | match_stacks_nil: forall bound1 bound
        (MG: match_globalenvs F bound1)
        (BELOW: Ple bound1 bound),
      match_stacks F m m' nil nil bound
  | match_stacks_cons: forall res f sp pc rs stk f' sp' rs' stk' bound fenv ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx f f'.(fn_code))
        (AG: agree_regs F ctx rs rs')
        (SP: F sp = Some(sp', ctx.(dstk)))
        (PRIV: range_private F m m' sp' (ctx.(dstk) + ctx.(mstk)) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RES: Ple res ctx.(mreg))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                   (Stackframe (sreg ctx res) f' (Vptr sp' Ptrofs.zero) (spc ctx pc) rs' :: stk')
                   bound
  | match_stacks_untailcall: forall stk res f' sp' rpc rs' stk' bound ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (PRIV: range_private F m m' sp' ctx.(dstk) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RET: ctx.(retinfo) = Some (rpc, res))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   stk
                   (Stackframe res f' (Vptr sp' Ptrofs.zero) rpc rs' :: stk')
                   bound

with match_stacks_inside (F: meminj) (m m': mem):
        list stackframe -> list stackframe -> function -> context -> block -> regset -> Prop :=
  | match_stacks_inside_base: forall stk stk' f' ctx sp' rs'
        (MS: match_stacks F m m' stk stk' sp')
        (RET: ctx.(retinfo) = None)
        (DSTK: ctx.(dstk) = 0),
      match_stacks_inside F m m' stk stk' f' ctx sp' rs'
  | match_stacks_inside_inlined: forall res f sp pc rs stk stk' f' fenv ctx sp' rs' ctx'
        (MS: match_stacks_inside F m m' stk stk' f' ctx' sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx' f f'.(fn_code))
        (AG: agree_regs F ctx' rs rs')
        (SP: F sp = Some(sp', ctx'.(dstk)))
        (PAD: range_private F m m' sp' (ctx'.(dstk) + ctx'.(mstk)) ctx.(dstk))
        (RES: Ple res ctx'.(mreg))
        (RET: ctx.(retinfo) = Some (spc ctx' pc, sreg ctx' res))
        (BELOW: context_below ctx' ctx)
        (SBELOW: context_stack_call ctx' ctx),
      match_stacks_inside F m m' (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                                 stk' f' ctx sp' rs'.(** ** Relating stacks *)

Inductive match_stacks (F: meminj) (m m': mem):
             list stackframe -> list stackframe -> block -> Prop :=
  | match_stacks_nil: forall bound1 bound
        (MG: match_globalenvs F bound1)
        (BELOW: Ple bound1 bound),
      match_stacks F m m' nil nil bound
  | match_stacks_cons: forall res f sp pc rs stk f' sp' rs' stk' bound fenv ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx f f'.(fn_code))
        (AG: agree_regs F ctx rs rs')
        (SP: F sp = Some(sp', ctx.(dstk)))
        (PRIV: range_private F m m' sp' (ctx.(dstk) + ctx.(mstk)) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RES: Ple res ctx.(mreg))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                   (Stackframe (sreg ctx res) f' (Vptr sp' Ptrofs.zero) (spc ctx pc) rs' :: stk')
                   bound
  | match_stacks_untailcall: forall stk res f' sp' rpc rs' stk' bound ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (PRIV: range_private F m m' sp' ctx.(dstk) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RET: ctx.(retinfo) = Some (rpc, res))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   stk
                   (Stackframe res f' (Vptr sp' Ptrofs.zero) rpc rs' :: stk')
                   bound

with match_stacks_inside (F: meminj) (m m': mem):
        list stackframe -> list stackframe -> function -> context -> block -> regset -> Prop :=
  | match_stacks_inside_base: forall stk stk' f' ctx sp' rs'
        (MS: match_stacks F m m' stk stk' sp')
        (RET: ctx.(retinfo) = None)
        (DSTK: ctx.(dstk) = 0),
      match_stacks_inside F m m' stk stk' f' ctx sp' rs'
  | match_stacks_inside_inlined: forall res f sp pc rs stk stk' f' fenv ctx sp' rs' ctx'
        (MS: match_stacks_inside F m m' stk stk' f' ctx' sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx' f f'.(fn_code))
        (AG: agree_regs F ctx' rs rs')
        (SP: F sp = Some(sp', ctx'.(dstk)))
        (PAD: range_private F m m' sp' (ctx'.(dstk) + ctx'.(mstk)) ctx.(dstk))
        (RES: Ple res ctx'.(mreg))
        (RET: ctx.(retinfo) = Some (spc ctx' pc, sreg ctx' res))
        (BELOW: context_below ctx' ctx)
        (SBELOW: context_stack_call ctx' ctx),
      match_stacks_inside F m m' (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                                 stk' f' ctx sp' rs'.(** ** Relating stacks *)

Inductive match_stacks (F: meminj) (m m': mem):
             list stackframe -> list stackframe -> block -> Prop :=
  | match_stacks_nil: forall bound1 bound
        (MG: match_globalenvs F bound1)
        (BELOW: Ple bound1 bound),
      match_stacks F m m' nil nil bound
  | match_stacks_cons: forall res f sp pc rs stk f' sp' rs' stk' bound fenv ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx f f'.(fn_code))
        (AG: agree_regs F ctx rs rs')
        (SP: F sp = Some(sp', ctx.(dstk)))
        (PRIV: range_private F m m' sp' (ctx.(dstk) + ctx.(mstk)) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RES: Ple res ctx.(mreg))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                   (Stackframe (sreg ctx res) f' (Vptr sp' Ptrofs.zero) (spc ctx pc) rs' :: stk')
                   bound
  | match_stacks_untailcall: forall stk res f' sp' rpc rs' stk' bound ctx
        (MS: match_stacks_inside F m m' stk stk' f' ctx sp' rs')
        (PRIV: range_private F m m' sp' ctx.(dstk) f'.(fn_stacksize))
        (SSZ1: 0 <= f'.(fn_stacksize) < Ptrofs.max_unsigned)
        (SSZ2: forall ofs, Mem.perm m' sp' ofs Max Nonempty -> 0 <= ofs <= f'.(fn_stacksize))
        (RET: ctx.(retinfo) = Some (rpc, res))
        (BELOW: Plt sp' bound),
      match_stacks F m m'
                   stk
                   (Stackframe res f' (Vptr sp' Ptrofs.zero) rpc rs' :: stk')
                   bound

with match_stacks_inside (F: meminj) (m m': mem):
        list stackframe -> list stackframe -> function -> context -> block -> regset -> Prop :=
  | match_stacks_inside_base: forall stk stk' f' ctx sp' rs'
        (MS: match_stacks F m m' stk stk' sp')
        (RET: ctx.(retinfo) = None)
        (DSTK: ctx.(dstk) = 0),
      match_stacks_inside F m m' stk stk' f' ctx sp' rs'
  | match_stacks_inside_inlined: forall res f sp pc rs stk stk' f' fenv ctx sp' rs' ctx'
        (MS: match_stacks_inside F m m' stk stk' f' ctx' sp' rs')
        (COMPAT: fenv_compat prog fenv)
        (FB: tr_funbody fenv f'.(fn_stacksize) ctx' f f'.(fn_code))
        (AG: agree_regs F ctx' rs rs')
        (SP: F sp = Some(sp', ctx'.(dstk)))
        (PAD: range_private F m m' sp' (ctx'.(dstk) + ctx'.(mstk)) ctx.(dstk))
        (RES: Ple res ctx'.(mreg))
        (RET: ctx.(retinfo) = Some (spc ctx' pc, sreg ctx' res))
        (BELOW: context_below ctx' ctx)
        (SBELOW: context_stack_call ctx' ctx),
      match_stacks_inside F m m' (Stackframe res f (Vptr sp Ptrofs.zero) pc rs :: stk)
                                 stk' f' ctx sp' rs'.

Lemma match_stacks_empty: forall stk stk' bound, match_stacks F m m' stk stk' bound -> stk = nil -> stk' = nil with match_stacks_inside_empty: forall stk stk' f ctx sp rs, match_stacks_inside F m m' stk stk' f ctx sp rs -> stk = nil -> stk' = nil /\ ctx.(retinfo) = None.