let x1, x2, x3, x4, x5, x6 be set ; :: thesis: card {x1,x2,x3,x4,x5,x6} <= 6
( card {x1} = 1 & {x1,x2,x3,x4,x5,x6} = {x1} \/ {x2,x3,x4,x5,x6} & {x1} is finite & {x2,x3,x4,x5,x6} is finite & card {x2,x3,x4,x5,x6} <= 5 ) by Th72, CARD_1:50, ENUMSET1:51;
then ( 1 + (card {x2,x3,x4,x5,x6}) <= 1 + 5 & card {x1,x2,x3,x4,x5,x6} <= 1 + (card {x2,x3,x4,x5,x6}) ) by Th62, XREAL_1:9;
hence card {x1,x2,x3,x4,x5,x6} <= 6 by XXREAL_0:2; :: thesis: verum