reserve x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2,z2,z4 for object;

theorem
 for a,b being triple object
   st a`1_3 = b`1_3 & a`2_3 = b`2_3 & a`3_3 = b`3_3
  holds a = b
proof let a,b be triple object such that
A1: a`1_3 = b`1_3 & a`2_3 = b`2_3 & a`3_3 = b`3_3;
  a = [a`1_3,a`2_3,a`3_3] & b = [b`1_3,b`2_3,b`3_3];
 hence a = b by A1;
end;
