let x1, x2, x3, x4, x5, x6, x7, x8 be object ; :: thesis: card {x1,x2,x3,x4,x5,x6,x7,x8} <= 8
card {x2,x3,x4,x5,x6,x7,x8} <= 7 by Th54;
then A1: 1 + (card {x2,x3,x4,x5,x6,x7,x8}) <= 1 + 7 by XREAL_1:7;
( {x1,x2,x3,x4,x5,x6,x7,x8} = {x1} \/ {x2,x3,x4,x5,x6,x7,x8} & card {x1} = 1 ) by CARD_1:30, ENUMSET1:22;
then card {x1,x2,x3,x4,x5,x6,x7,x8} <= 1 + (card {x2,x3,x4,x5,x6,x7,x8}) by Th42;
hence card {x1,x2,x3,x4,x5,x6,x7,x8} <= 8 by A1, XXREAL_0:2; :: thesis: verum