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
  UsedILoc(p +* r) c= UsedILoc p \/ UsedILoc r
proof
   rng(p +* r) c= rng p \/ rng r by FUNCT_4:17;
   then UsedILoc(p +* r) c= UsedILoc(rng p \/ rng r) by Lm2;
  hence UsedILoc(p +* r) c= UsedILoc p \/ UsedILoc r by Lm3;
end;
