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 Th37:
  dom p misses dom r implies UsedI*Loc (p +* r) = (UsedI*Loc p
  ) \/ (UsedI*Loc r)
proof
 assume dom p misses dom r;
  then rng(p +* r) = rng p \/ rng r by NECKLACE:6;
  then UsedI*Loc(p +* r) = UsedI*Loc(rng p \/ rng r);
 hence UsedI*Loc(p +* r) = UsedI*Loc p \/ UsedI*Loc r by Lm6;
end;
