reserve a,b,c,d for set,
  D,X1,X2,X3,X4 for non empty set,
  x1,y1,z1 for Element of X1,
  x2 for Element of X2,
  x3 for Element of X3,
  x4 for Element of X4,
  A1,B1 for Subset of X1;
reserve x,y for Element of [:X1,X2,X3:];

theorem
  b =x`2_3 iff for x1,x2,x3 st x = [x1,x2,x3] holds b = x2
by MCART_1:66;
