reserve FT for non empty RelStr,
  A,B,C for Subset of FT;

theorem
  for A being Subset of FT, x being Element of FT st x in A holds <*x*>
  is_minimum_path_in A,x,x
proof
  let A be Subset of FT, x be Element of FT;
  assume
A1: x in A;
  thus <*x*> is continuous;
  {x} c= A by A1,ZFMISC_1:31;
  hence rng <*x*> c= A by FINSEQ_1:38;
  len <*x*> =1 by FINSEQ_1:40;
  hence thesis;
end;
