reserve X for RealUnitarySpace;
reserve x, y, z, g, g1, g2 for Point of X;
reserve a, q, r for Real;
reserve seq, seq1, seq2, seq9 for sequence of X;
reserve k, n, m, m1, m2 for Nat;

theorem
  r > 0 implies x in Ball(x,r)
proof
A1: dist(x,x) = 0 by BHSP_1:34;
  assume r > 0;
  hence thesis by A1,Th41;
end;
