theorem Th52:
  card {x1,x2,x3,x4,x5} <= 5
proof
  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 thesis by A1,XXREAL_0:2;
end;
