reserve z,z1,z2,z3,z4 for Element of F_Complex;

theorem
  |.z1 - z2.| <= |.z1 - z.| + |.z - z2.|
proof
  reconsider z9=z,z19=z1,z29=z2 as Element of COMPLEX by Def1;
A1: z9 - z29 = z - z2 by Th3;
  |.z19 - z29.| = |.z1 - z2.| & |.z19 - z9.| = |.z1 - z.| by Th3;
  hence thesis by A1,COMPLEX1:63;
end;
