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

theorem Th43:
  for I,J being Program 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 Program of SCM+FSA;
  let a be Int-Location;
  assume that
A1: I does not destroy a and
A2: J does not destroy a;
A3: Reloc(J,card I) does not destroy a by A2,SCMFSA8A:9;
A4: I ";" J
    = CutLastLoc stop Directed I +* Reloc(J,card stop I -' 1) by SCMFSA6A:37
   .= Directed I +* Reloc(J,card I) by COMPOS_1:71;
  Directed I does not destroy a by A1,SCMFSA8A:13;
  hence thesis by A3,A4,SCMFSA8A:11;
end;
