let x1, x2, x3, x4, x5 be object ; 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; verum