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 Th4:
  {} in F
proof
  consider A being Subset of X such that
A1: A in F by SUBSET_1:4;
  A misses A` by XBOOLE_1:79;
  then
A2: A /\ A` = {} by XBOOLE_0:def 7;
  A` in F by A1,Def1;
  hence thesis by A1,A2,FINSUB_1:def 2;
end;
