
theorem Th3:
  for n being Element of NAT, A being Subset of TOP-REAL n, p, q
  being Point of TOP-REAL n st A is_an_arc_of p, q holds A \ {p} is non empty
proof
  let n be Element of NAT, A be Subset of TOP-REAL n, p, q be Point of
  TOP-REAL n;
  assume A is_an_arc_of p, q;
  then
A1: A \ { p, q } <> {} by JORDAN6:43;
  { p } c= { p, q } by ZFMISC_1:7;
  hence thesis by A1,XBOOLE_1:3,34;
end;
