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;
