reserve m for Nat;
reserve P for Instruction-Sequence of SCM+FSA;

theorem Th6:
  for I being preProgram of SCM+FSA, a being Int-Location
  st I does not destroy a
 holds Directed I does not destroy a
proof
  let I be preProgram of SCM+FSA;
  let a be Int-Location;
  assume
A1: I does not destroy a;
  now
    let i be Instruction of SCM+FSA;
A2: dom Directed I = dom I by FUNCT_4:99;
    assume i in rng Directed I;
    then consider x being object such that
A3: x in dom Directed I and
A4: i = (Directed I).x by FUNCT_1:def 3;
    per cases;
    suppose
      I.x <> halt SCM+FSA;
      then i = I.x by A4,FUNCT_4:105;
      then i in rng I by A3,A2,FUNCT_1:def 3;
      hence i does not destroy a by A1,SCMFSA7B:def 4;
    end;
    suppose
      I.x = halt SCM+FSA;
      then i = goto card I by A3,A4,A2,FUNCT_4:106;
      hence i does not destroy a by SCMFSA7B:11;
    end;
  end;
  hence thesis by SCMFSA7B:def 4;
end;
