theorem Th38:
  for i being Nat st 1 < i & i <= len f & f/.i = f/.1
  holds i = len f
proof
  let i be Nat such that
A1: 1 < i and
A2: i <= len f and
A3: f/.i = f/.1;
  assume i <> len f;
  then i < len f by A2,XXREAL_0:1;
  hence contradiction by A1,A3,Th36;
end;
