reserve n for Element of NAT,
  i for Integer,
  a, b, r for Real,
  x for Point of TOP-REAL n;

theorem Th12:
  for n being non zero Element of NAT, x being Point of TOP-REAL
  n holds x is Point of Tunit_circle(n) implies |. x .| = 1
proof
  reconsider j = 1 as non negative Real;
  let n be non zero Element of NAT, x be Point of TOP-REAL n;
  assume x is Point of Tunit_circle(n);
  then x in the carrier of Tcircle(0.TOP-REAL n,j);
  then x in Sphere(0.TOP-REAL n,1) by Th9;
  hence thesis by TOPREAL9:12;
end;
