reserve a, b, c, a1, a2, b1, b2 for Int-Location,
  l, l1, l2 for Nat,
  f, g, f1, f2 for FinSeq-Location,
  i, j for Instruction of SCM+FSA,
  X, Y for set;
reserve p, r for preProgram of SCM+FSA,
  I, J for Program of SCM+FSA,
  k, m, n for Nat;

theorem Th43:
  UsedI*Loc (I ";" J) = UsedI*Loc I \/ UsedI*Loc J
proof
A1: card(stop Directed I) -' 1 = card Directed I by COMPOS_1:71
      .= card I by SCMFSA6A:36;
  dom I = dom Directed I by FUNCT_4:99;
  then
A2: dom Directed I misses dom (Reloc(J, card I)) by COMPOS_1:48;
  thus UsedI*Loc (I ";" J)
     = UsedI*Loc(stop Directed I ';' J)
    .= UsedI*Loc Directed I \/ UsedI*Loc Reloc(J, card I) by A2,Th37,A1
    .= (UsedI*Loc I) \/ UsedI*Loc Reloc(J, card I) by Th42
    .= (UsedI*Loc I) \/ (UsedI*Loc J) by Th41;
end;
