theorem
 for X1,X2,X3,X4 being non empty set
 for x being Element of [:X1,X2,X3,X4:]
 st for xx1 being Element of X1,
             xx2 being Element of X2,
             xx3 being Element of X3,
             xx4 being Element of X4 st x = [xx1,
  xx2,xx3,xx4] holds y2 = xx2
 holds y2 =x`2_4
proof
 let X1,X2,X3,X4 be non empty set;
 let x be Element of [:X1,X2,X3,X4:];
  assume that
A1: for xx1 being Element of X1,
             xx2 being Element of X2,
             xx3 being Element of X3,
             xx4 being Element of X4 st x = [xx1,xx2,xx3,xx4] holds y2 = xx2;
  x = [x`1_4,x`2_4,x`3_4,x`4_4];
  hence thesis by A1;
end;
