let x1, x2, x3, x4, x5, x6, x7 be object ; :: thesis: card {x1,x2,x3,x4,x5,x6,x7} <= 7
card {x2,x3,x4,x5,x6,x7} <= 6 by Th53;
then A1: 1 + (card {x2,x3,x4,x5,x6,x7}) <= 1 + 6 by XREAL_1:7;
( card {x1} = 1 & {x1,x2,x3,x4,x5,x6,x7} = {x1} \/ {x2,x3,x4,x5,x6,x7} ) by CARD_1:30, ENUMSET1:16;
then card {x1,x2,x3,x4,x5,x6,x7} <= 1 + (card {x2,x3,x4,x5,x6,x7}) by Th42;
hence card {x1,x2,x3,x4,x5,x6,x7} <= 7 by A1, XXREAL_0:2; :: thesis: verum