theorem Th22:
  a <> b implies StoneH(L).a <> StoneH(L).b
proof
  assume a <> b;
  then not a [= b or not b [= a by LATTICES:8;
  then (ex F st F in F_primeSet(L) & not b in F & a in F) or ex F st F in
  F_primeSet(L) & not a in F & b in F by Th20;
  then consider F such that
A1: F in F_primeSet(L) and
A2: b in F & not a in F or a in F & not b in F;
  F in StoneH(L).a & not F in StoneH(L).b or F in StoneH(L).b & not F in
  StoneH(L).a by A1,A2,Th11;
  hence thesis;
end;
