reserve x for set;
reserve a, b, c for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p, q for Rational;
reserve s1, s2 for Real_Sequence;

theorem Th37:
  1 #Z k = 1
proof
  per cases;
  suppose
    k>=0;
    hence 1 #Z k = 1 |^ |.k.| by Def3
      .= 1;
  end;
  suppose
    k<0;
    1 #Z k = (1 |^ |.k.|)" by Def3;
    hence thesis;
  end;
end;
