Let pred_nat_unfolded_subproof px :
Pos.to_nat px <> 0.

Lemma minus_pred_nat :
forall (n m : Z) (Hn : (0 < n)%Z) (Hm : (0 < m)%Z) (Hnm : (0 < n - m)%Z),
S (pred_nat n Hn) - S (pred_nat m Hm) = S (pred_nat (n - m) Hnm).