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;
reserve L for finite Subset of Int-Locations;
reserve L for finite Subset of FinSeq-Locations;

theorem Th57:
  not First*NotUsed p in UsedI*Loc p
proof
  ex sil being finite Subset of FinSeq-Locations st sil = UsedI*Loc p &
  First*NotUsed p = First*NotIn sil by Def8;
  hence thesis by SCMFSA_M:16;
end;
