theorem
  [:X1,X2,X3:] meets [:Y1,Y2,Y3:] implies X1 meets Y1 & X2 meets Y2 & X3
  meets Y3
proof
  assume
A1: [:X1,X2,X3:] meets [:Y1,Y2,Y3:];
A2: [:[:X1,X2:],X3:] = [:X1,X2,X3:] & [:[:Y1,Y2:],Y3:] = [:Y1,Y2,Y3:] by
ZFMISC_1:def 3;
  then [:X1,X2:] meets [:Y1,Y2:] by A1,ZFMISC_1:104;
  hence thesis by A2,A1,ZFMISC_1:104;
end;
