reserve R for non empty RelStr,
  N for net of R,
  i for Element of N;

theorem Th32:
  for T being complete Scott TopLattice
  holds the TopStruct of T = ConvergenceSpace Scott-Convergence T
proof
  let T be complete Scott TopLattice;
  set CSC = ConvergenceSpace Scott-Convergence T;
  the topology of T = the topology of CSC
  proof
    thus the topology of T c= the topology of CSC
    proof
      let e be object;
      assume
A1:   e in the topology of T;
      then reconsider A = e as Subset of T;
      A is open by A1;
      then A is inaccessible upper by Def4;
      hence thesis by Th31;
    end;
    let e be object;
    assume
A2: e in the topology of CSC;
    then reconsider A = e as Subset of T by YELLOW_6:def 24;
    A is inaccessible upper by A2,Th31;
    then A is open by Def4;
    hence thesis;
  end;
  hence thesis by YELLOW_6:def 24;
end;
