reserve Omega for set;
reserve X, Y, Z, p,x,y,z for set;
reserve D, E for Subset of Omega;
reserve f for Function;
reserve m,n for Nat;
reserve r,r1 for Real;
reserve seq for Real_Sequence;
reserve F for Field_Subset of X;

theorem Th5:
  X in F
proof
  consider A being Subset of X such that
A1: A in F by SUBSET_1:4;
A2: A \/ A` = [#] X by SUBSET_1:10
    .= X;
  A` in F by A1,Def1;
  hence thesis by A1,A2,Th3;
end;
