  We determine the strictly positive fragment $\mathsf{QPL}^+(\mathsf{HA})$ of
the quantified provability logic $\mathsf{QPL}(\mathsf{HA})$ of Heyting
Arithmetic. We show that $\mathsf{QPL}^+(\mathsf{HA})$ is decidable and that it
coincides with $\mathsf{QPL}^+(\mathsf{PA})$, which is the strictly positive
fragment of the quantified provability logic of of Peano Arithmetic. This
positively resolves a previous conjecture of the authors.
  On our way to proving these results, we carve out the strictly positive
fragment $\mathsf{PL}^+(\mathsf{HA})$ of the provability logic
$\mathsf{PL}(\mathsf{HA})$ of Heyting Arithmetic, provide a simple
axiomatization, and prove it to be sound and complete for two types of
arithmetical interpretations.
  The simple fragments presented in this paper should be contrasted with a 2022
result by Mojtahedi, where an axiomatization for $\mathsf{PL}(\mathsf{HA})$ is
provided. This axiomatization, although decidable, is of considerable
complexity.
