let X1, X2, X3, X4, X5, X6, X7, X8, X9, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9 be set ; :: thesis: ( [:X1,X2,X3,X4,X5,X6,X7,X8,X9:] meets [:Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8,Y9:] implies ( X1 meets Y1 & X2 meets Y2 & X3 meets Y3 & X4 meets Y4 & X5 meets Y5 & X6 meets Y6 & X7 meets Y7 & X8 meets Y8 & X9 meets Y9 ) )
assume A1: [:X1,X2,X3,X4,X5,X6,X7,X8,X9:] meets [:Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8,Y9:] ; :: thesis: ( X1 meets Y1 & X2 meets Y2 & X3 meets Y3 & X4 meets Y4 & X5 meets Y5 & X6 meets Y6 & X7 meets Y7 & X8 meets Y8 & X9 meets Y9 )
A2: ( [:X1,X2,X3,X4,X5,X6,X7,X8:] = [:[:[:[:[:[:[:X1,X2:],X3:],X4:],X5:],X6:],X7:],X8:] & [:[:[:[:[:[:[:Y1,Y2:],Y3:],Y4:],Y5:],Y6:],Y7:],Y8:] = [:Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8:] ) by Th126;
( [:[:[:[:[:[:[:[:X1,X2:],X3:],X4:],X5:],X6:],X7:],X8:],X9:] = [:X1,X2,X3,X4,X5,X6,X7,X8,X9:] & [:[:[:[:[:[:[:[:Y1,Y2:],Y3:],Y4:],Y5:],Y6:],Y7:],Y8:],Y9:] = [:Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8,Y9:] ) by Th169;
then [:[:[:[:[:[:[:X1,X2:],X3:],X4:],X5:],X6:],X7:],X8:] meets [:[:[:[:[:[:[:Y1,Y2:],Y3:],Y4:],Y5:],Y6:],Y7:],Y8:] by A1, ZFMISC_1:104;
hence ( X1 meets Y1 & X2 meets Y2 & X3 meets Y3 & X4 meets Y4 & X5 meets Y5 & X6 meets Y6 & X7 meets Y7 & X8 meets Y8 & X9 meets Y9 ) by A2, A1, Th141, ZFMISC_1:104; :: thesis: verum