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
  UsedI*Loc (p +* r) c= UsedI*Loc p \/ UsedI*Loc r
proof
   rng(p +* r) c= rng p \/ rng r by FUNCT_4:17;
   then UsedI*Loc(p +* r) c= UsedI*Loc(rng p \/ rng r) by Lm5;
  hence UsedI*Loc(p +* r) c= UsedI*Loc p \/ UsedI*Loc r by Lm6;
end;
