reserve z1,z2,z3,z4,z for Quaternion;

theorem
  |.z1-z2-z3.| <= |.z1.| + |.z2.| + |.z3.|
proof
  |.z1 - z2-z3.|<=|.z1-z2.|+|.z3.| & |.z1-z2.|<=|.z1.|+|.z2.|
    by QUATERNI:80;
  then |.z1 - z2-z3.|+ |.z1-z2.|<=|.z1-z2.|+|.z3.|+(|.z1.|+|.z2.|)
    by XREAL_1:7; then
  |.z1 - z2-z3.|<=|.z1-z2.|+|.z3.|+(|.z1.|+|.z2.|)-|.z1-z2.| by XREAL_1:19;
  hence thesis;
end;
