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;

theorem Th50:
  not FirstNotUsed p in UsedILoc p
proof
  consider sil being finite Subset of Int-Locations such that
A1: sil = UsedILoc p \/ {intloc 0} and
A2: FirstNotUsed p = FirstNotIn sil by Def7;
  not FirstNotUsed p in sil by A2,SCMFSA_M:14;
  hence thesis by A1,XBOOLE_0:def 3;
end;
