
theorem
  for n, A, B, N being Nat st Fusc N = A * Fusc (2*n) + B * Fusc (2*n+1)
  holds Fusc N = (A+B) * Fusc n + B * Fusc (n+1)
proof
  let n, A, B, N be Nat such that
A1: Fusc N = A * Fusc (2*n) + B * Fusc (2*n+1);
  Fusc (2*n+1) = Fusc n + Fusc (n+1) by Th15;
  hence Fusc N = A*Fusc n+(B*Fusc n +B*Fusc (n+1)) by A1,Th15
    .= (A+B)*Fusc n + B*Fusc (n+1);
end;
