
theorem Th15:
  for D being non empty set, f being FinSequence of D
  st 1 <= len f holds f is_odd_substring_of f,0
proof
  let D be non empty set, f be FinSequence of D;
  assume A1: 1 <= len f;
  now
    assume len f > 0;
    reconsider i = 1 as odd Element of NAT by POLYFORM:4;
    take i;
    thus 0 <= i;
    thus i <= len f by A1;
    thus mid(f,i,(i-'1)+len f) = mid(f,i,0+len f) by XREAL_1:232
      .= f by A1, FINSEQ_6:120;
  end;
  hence thesis;
end;
