reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;
reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 for Element of X;
reserve x for object;

theorem
  X <> {} implies {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10} is Subset of X
proof
  set A = {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10};
  assume
A1: X <> {};
  A c= X
  proof
    let x be object;
    x in A implies x=x1 or x=x2 or x=x3 or x=x4 or x=x5 or x=x6 or x=x7 or
    x=x8 or x=x9 or x=x10 by ENUMSET1:def 8;
    hence thesis by A1,Def1;
  end;
  then A in bool X by ZFMISC_1:def 1;
  hence thesis by Def1;
end;
