theorem Th20:
  p in Domin_0(n,m) iff p is dominated_by_0 & dom p = n & Sum p = m
proof
  thus p in Domin_0(n,m) implies p is dominated_by_0 & dom p=n & Sum p=m
  proof
    assume p in Domin_0(n,m);
    then ex q st q=p & q is dominated_by_0 & dom q = n & Sum q = m by Def2;
    hence thesis;
  end;
  thus thesis by Def2;
end;
