theorem Th50:
  for A being non empty Subset of TOP-REAL n, p,q being Point of
  TOP-REAL n st q in A holds dist(p,A) <= dist(p,q)
proof
  let A be non empty Subset of TOP-REAL n;
  let p,q be Point of TOP-REAL n;
  assume q in A;
  then {q} c= A by ZFMISC_1:31;
  then dist(p,A) <= dist(p,{q}) by Th41;
  hence thesis by Th43;
end;
