theorem Th53:
  card {x1,x2,x3,x4,x5,x6} <= 6
proof
  card {x2,x3,x4,x5,x6} <= 5 by Th52;
  then
A1: 1 + card {x2,x3,x4,x5,x6} <= 1+5 by XREAL_1:7;
  card {x1} = 1 & {x1,x2,x3,x4,x5,x6} = {x1} \/ {x2,x3,x4,x5,x6} by CARD_1:30
,ENUMSET1:11;
  then card {x1,x2,x3,x4,x5,x6} <= 1 + card {x2,x3,x4,x5,x6} by Th42;
  hence thesis by A1,XXREAL_0:2;
end;
