reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem Th62:
  for f being FinSequence holds f.1 = (Rev f).(len f) & f.(len f) = (Rev f).1
proof
  let f be FinSequence;
  per cases;
  suppose
A1: f is empty;
    hence f.1 = {}
      .= (Rev f).(len f) by A1;
    thus f.(len f) = {} by A1
      .= (Rev f).1 by A1;
  end;
  suppose
A3: f is non empty;
    then len f in Seg len f by FINSEQ_1:3;
    then len f in dom f by FINSEQ_1:def 3;
    hence (Rev f).(len f) = f.(len f - len f + 1) by Th58
      .= f.1;
    len f >= 1 by A3,NAT_1:14;
    then 1 in dom f by FINSEQ_3:25;
    hence (Rev f).1 = f.(len f - 1 + 1) by Th58
      .= f.(len f);
  end;
end;
