Section ExMinn.
Variable P : pred nat.
Hypothesis exP : exists n, P n.
Inductive acc_nat i : Prop := AccNat0 of P i | AccNatS of acc_nat i.+1.
Definition ex_minn := s2val find_ex_minn.
Inductive ex_minn_spec : nat -> Type :=
ExMinnSpec m of P m & (forall n, P n -> n >= m) : ex_minn_spec m.
End ExMaxn.

Lemma eq_ex_maxn (P Q : pred nat) m n exP ubP exQ ubQ :
P =1 Q -> @ex_maxn P m exP ubP = @ex_maxn Q n exQ ubQ.