reserve X for TopSpace;
reserve X for non empty TopSpace;
reserve X1, X2, X3 for non empty SubSpace of X;
reserve X1, X2, X3 for non empty SubSpace of X;
reserve X for TopSpace;
reserve A1, A2 for Subset of X;

theorem Th36:
  A1 misses A2 & A1 is open implies A1 misses Cl A2
proof
  assume
A1: A1 misses A2;
  thus A1 is open implies A1 misses Cl A2
  proof
    assume
A2: A1 is open;
    A2 c= A1` by A1,SUBSET_1:23;
    then Cl A2 c= A1` by A2,TOPS_1:5;
    then Cl A2 misses A1`` by SUBSET_1:24;
    hence thesis;
  end;
end;
