let x1, x2, x3, x4, x5 be object ; :: thesis: card {x1,x2,x3,x4,x5} <= 5
card {x2,x3,x4,x5} <= 4 by Th51;
then A1: 1 + (card {x2,x3,x4,x5}) <= 1 + 4 by XREAL_1:7;
( card {x1} = 1 & {x1,x2,x3,x4,x5} = {x1} \/ {x2,x3,x4,x5} ) by CARD_1:30, ENUMSET1:7;
then card {x1,x2,x3,x4,x5} <= 1 + (card {x2,x3,x4,x5}) by Th42;
hence card {x1,x2,x3,x4,x5} <= 5 by A1, XXREAL_0:2; :: thesis: verum