reserve m for Nat;
reserve P,PP,P1,P2 for Instruction-Sequence of SCM+FSA;

theorem Th52:
  for s being State of SCM+FSA,
      I being parahalting really-closed Program of
  SCM+FSA, a being Int-Location,k being Element of NAT st I does not destroy a
holds IExec(I,P,s).a = Comput(P +* I,(Initialize Initialized s),k).a
proof
  let s be State of SCM+FSA;
  let I be parahalting really-closed Program of SCM+FSA;
  let a be Int-Location;
  let k be Element of NAT;
  set s0 = Initialized s;
  set s1 = Initialize s0,
      P1 = P +* I;
A1: I c= P1 by FUNCT_4:25;
  P1 halts_on s1 by A1,SCMFSA6B:1;
  then I is_halting_on s0,P;
  hence thesis by Th51;
end;
