theorem
  for L be eigenvalue of id V holds L = 1_K
proof
  let L be eigenvalue of id V;
  id V is with_eigenvalues by Th11;
  then consider v be Vector of V such that
A1: v<>0.V and
A2: id V.v = L*v by Def2;
  L*v = v by A2
    .= 1_K*v;
  hence thesis by A1,VECTSP10:4;
end;
