reserve L for Lattice,
  p,p1,q,q1,r,r1 for Element of L;
reserve x,y,z,X,Y,Z,X1,X2 for set;
reserve H,F for Filter of L;
reserve D for non empty Subset of L;
reserve D1,D2 for non empty Subset of L;
reserve I for I_Lattice,
  i,j,k for Element of I;
reserve B for B_Lattice,
  FB,HB for Filter of B;
reserve I for I_Lattice,
  i,j,k for Element of I,
  DI for non empty Subset of I,
  FI for Filter of I;

theorem Th29:
  i in FI & i => j in FI implies j in FI
proof
  assume i in FI & i => j in FI;
  then
A1: i "/\" (i => j) in FI by Th8;
  i "/\" (i => j) [= j by Def7;
  hence thesis by A1,Th9;
end;
