reserve v,x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2 for object,
  X,X1,X2,X3,X4,Y,Y1,Y2,Y3,Y4,Y5,
  Z,Z1,Z2,Z3,Z4,Z5 for set;
reserve p for pair object;
reserve R for Relation;
reserve xx1 for Element of X1,
  xx2 for Element of X2,
  xx3 for Element of X3;
reserve xx4 for Element of X4;

theorem
  [:X1,X2,X3,X4:] meets [:Y1,Y2,Y3,Y4:] implies X1 meets Y1 & X2 meets
  Y2 & X3 meets Y3 & X4 meets Y4
proof
  assume
A1: [:X1,X2,X3,X4:] meets [:Y1,Y2,Y3,Y4:];
A2: [:[:[:X1,X2:],X3:],X4:] = [:X1,X2,X3,X4:] & [:[:[:Y1,Y2:],Y3:],Y4:] = [:
  Y1, Y2,Y3,Y4:] by Th37;
  then
A3: [:[:X1,X2:],X3:] meets [:[:Y1,Y2:],Y3:] by A1,ZFMISC_1:104;
  then [:X1,X2:] meets [:Y1,Y2:] by ZFMISC_1:104;
  hence thesis by A2,A1,A3,ZFMISC_1:104;
end;
