reserve L,L1,L2 for Lattice,
  F1,F2 for Filter of L,
  p,q,r,s for Element of L,
  p1,q1,r1,s1 for Element of L1,
  p2,q2,r2,s2 for Element of L2,
  X,x,x1,x2,y,y1,y2 for set,
  D,D1,D2 for non empty set,
  R for Relation,
  RD for Equivalence_Relation of D,
  a,b,d for Element of D,
  a1,b1,c1 for Element of D1,
  a2,b2,c2 for Element of D2,
  B for B_Lattice,
  FB for Filter of B,
  I for I_Lattice,
  FI for Filter of I ,
  i,i1,i2,j,j1,j2,k for Element of I,
  f1,g1 for BinOp of D1,
  f2,g2 for BinOp of D2;
reserve F,G for BinOp of D,RD;

theorem
  L1 is B_Lattice & L2 is B_Lattice iff [:L1,L2:] is B_Lattice
proof
A1: [:L1,L2:] is D_Lattice iff L1 is D_Lattice & L2 is D_Lattice by Th38;
  [:L1,L2:] is C_Lattice iff L1 is C_Lattice & L2 is C_Lattice by Th45;
  hence thesis by A1;
end;
