let X1, X2, X3, X4, Y1, Y2, Y3, Y4 be set ; :: thesis: ( [:X1,X2,X3,X4:] meets [:Y1,Y2,Y3,Y4:] implies ( X1 meets Y1 & X2 meets Y2 & X3 meets Y3 & X4 meets Y4 ) )
A1: ( [:[:[:X1,X2:],X3:],X4:] = [:X1,X2,X3,X4:] & [:[:[:Y1,Y2:],Y3:],Y4:] = [:Y1,Y2,Y3,Y4:] ) by Th53;
assume [:X1,X2,X3,X4:] meets [:Y1,Y2,Y3,Y4:] ; :: thesis: ( X1 meets Y1 & X2 meets Y2 & X3 meets Y3 & X4 meets Y4 )
then ( [:[:X1,X2:],X3:] meets [:[:Y1,Y2:],Y3:] & X4 meets Y4 ) by A1, ZFMISC_1:127;
then ( [:X1,X2:] meets [:Y1,Y2:] & X3 meets Y3 & X4 meets Y4 ) by ZFMISC_1:127;
hence ( X1 meets Y1 & X2 meets Y2 & X3 meets Y3 & X4 meets Y4 ) by ZFMISC_1:127; :: thesis: verum