
theorem Th15: :: Index01
  for p being non empty FinSequence,
      T being non empty Subset of rng p
  ex x being set st x in T & for y being set st y in T holds x..p <= y..p
proof
  let S be non empty FinSequence;
  let T be non empty Subset of rng S;
  deffunc F(set) = $1..S;
  consider m being Element of T such that
A1: for y being Element of T holds F(m) <= F(y) from PRE_CIRC:sch 5;
  take m;
  thus m in T;
  let y be set;
  assume y in T;
  hence thesis by A1;
end;
