reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;
reserve m,n for Nat;
reserve x1,x2,x3,x4,x5,x6,x7,x8 for object;

theorem Th51:
  card {x1,x2,x3,x4} <= 4
proof
  card {x2,x3,x4} <= 3 by Th50;
  then
A1: 1 + card {x2,x3,x4} <= 1+3 by XREAL_1:7;
  card {x1} = 1 & {x1,x2,x3,x4} = {x1} \/ {x2,x3,x4} by CARD_1:30,ENUMSET1:4;
  then card {x1,x2,x3,x4} <= 1 + card {x2,x3,x4 } by Th42;
  hence thesis by A1,XXREAL_0:2;
end;
