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

theorem Th4:
  for I,J being preProgram of SCM+FSA, a being Int-Location holds
  I does not destroy a & J does not destroy a implies I +* J does not destroy a
proof
  let I,J be preProgram of SCM+FSA;
  let a be Int-Location;
  assume
A1: I does not destroy a;
  assume
A2: J does not destroy a;
  now
    let i be Instruction of SCM+FSA;
A3: rng (I +* J) c= rng I \/ rng J by FUNCT_4:17;
    assume
A4: i in rng (I +* J);
    per cases by A4,A3,XBOOLE_0:def 3;
    suppose
      i in rng I;
      hence i does not destroy a by A1,SCMFSA7B:def 4;
    end;
    suppose
      i in rng J;
      hence i does not destroy a by A2,SCMFSA7B:def 4;
    end;
  end;
  hence thesis by SCMFSA7B:def 4;
end;
