reserve x,y,Y,Z for set,
  L for LATTICE,
  l for Element of L;

theorem ::3.14 (1-2), p.71
  for L being lower-bounded continuous LATTICE holds L is distributive
  iff L is Heyting
proof
  let L be lower-bounded continuous LATTICE;
  thus L is distributive implies L is Heyting
  proof
    assume L is distributive;
    then PRIME L is order-generating by Th35;
    then L is distributive meet-continuous by Th34;
    hence thesis;
  end;
  thus thesis;
end;
