reserve L for Lattice;
reserve X,Y,Z,V for Element of L;

theorem
  X = Y "/\" Z iff X [= Y & X [= Z & for V st V [= Y & V [= Z holds V [= X
proof
  thus X = Y "/\" Z implies X [= Y & X [= Z & for V st V [= Y & V [= Z holds V
  [= X by FILTER_0:7,LATTICES:6;
  assume that
A1: X [= Y & X [= Z and
A2: for V st V [= Y & V [= Z holds V [= X;
A3: X [= Y "/\" Z by A1,FILTER_0:7;
  Y "/\" Z [= Y & Y "/\" Z [= Z by LATTICES:6;
  then Y "/\" Z [= X by A2;
  hence thesis by A3;
end;
