let x1, x2, x3, x4, y1, y2, y3, y4 be object ; :: thesis: ( [[x1,x2],[x3,x4]] = [[y1,y2],[y3,y4]] implies ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 ) )
assume [[x1,x2],[x3,x4]] = [[y1,y2],[y3,y4]] ; :: thesis: ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 )
then ( [x1,x2] = [y1,y2] & [x3,x4] = [y3,y4] ) by XTUPLE_0:1;
hence ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 ) by XTUPLE_0:1; :: thesis: verum