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

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