reserve n for Nat;
reserve p for Point of TOP-REAL n, r for Real;

theorem Th5:
  n <> 0 & p is Point of Tunit_ball(n) implies |. p .| < 1
proof
  reconsider j = 1 as Real;
  assume n <> 0; then
  reconsider n1 = n as non zero Element of NAT by ORDINAL1:def 12;
  assume p is Point of Tunit_ball(n); then
  p in the carrier of Tball(0.(TOP-REAL n1),j);
  then p in Ball(0.(TOP-REAL n1),1) by MFOLD_0:2;
  hence thesis by TOPREAL9:10;
end;
