reserve X,Y,Z,X1,X2,X3,X4,X5,X6 for set, x,y for object;
reserve a,b,c for object, X,Y,Z,x,y,z for set;
reserve A,B,C,D for Ordinal;
reserve F,G for Function;
reserve L,L1 for Sequence;

theorem
  A c< B or A = B or B c< A
proof
  assume that
A1: not A c< B & not A = B and
A2: not B c< A;
  not A c= B by A1;
  hence contradiction by A2;
end;
