include "LTL/LTLToLIN.ma".
include "LTL/LTL_semantics.ma".
include "LIN/LIN_semantics.ma".
include "joint/Traces.ma".
include "common/StatusSimulation.ma".

(* this should come directly from linearise proof *)
axiom LTLToLIN_ok :
∀stacksizes : ident → option ℕ. (* are hypotheses needed here? *)
∀p_in : joint_program LTL.
let p_out ≝ ltl_to_lin p_in in
∃[1] R.
  status_simulation
    (joint_status LTL_semantics p_in stacksizes)
    (joint_status LIN_semantics p_out stacksizes)
    R ∧
  ∀init_in.make_initial_state
    (mk_prog_params LTL_semantics p_in stacksizes) = OK … init_in →
  ∃init_out.
    make_initial_state
     (mk_prog_params LIN_semantics p_out stacksizes) =
      OK ? init_out ∧
   R init_in init_out.