theorem Th54:
  card {x1,x2,x3,x4,x5,x6,x7} <= 7
proof
  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 thesis by A1,XXREAL_0:2;
end;
