theorem Th31:
  for p being Point of TOP-REAL 2 holds |.p.|<=|.p`1.|+|.p`2.|
proof
  let p be Point of TOP-REAL 2;
  (|.p.|)^2= (p`1)^2+(p`2)^2 by Th29;
  then sqrt((p`1)^2+(p`2)^2)=|.p.| by SQUARE_1:22;
  hence thesis by COMPLEX1:78;
end;
