 reserve L for Lattice;
 reserve I,P for non empty ClosedSubset of L;
reserve L for lower-bounded pseudocomplemented Lattice;

theorem
  for L being pseudocomplemented distributive lower-bounded Lattice holds
  for a, b being Element of L st a in Skeleton L & b in Skeleton L holds
  a "/\" b in Skeleton L
  proof
    let L be pseudocomplemented distributive lower-bounded Lattice;
    let a, b be Element of L;
    assume a in Skeleton L & b in Skeleton L; then
A2: a = a** & b = b** by Th13;
    a* [= (a "/\" b)* by Th6,LATTICES:6; then
B2: (a "/\" b)** [= a by A2,Th6;
    b* [= (a "/\" b)* by Th6,LATTICES:6; then
    (a "/\" b)** [= b** by Th6; then
B1: (a "/\" b)** [= a "/\" b by B2,FILTER_0:7,A2;
    a "/\" b [= (a "/\" b)** by Th5; then
    a "/\" b = (a "/\" b)** by B1,LATTICES:8;
    hence thesis;
  end;
