Section Extremum.
Context {T : eqType} {I : finType} (ord : rel T).
Context (i0 : I) (P : pred I) (F : I -> T).
Definition extremum := odflt i0 (pick (arg_pred ord P F)).
Hypothesis ord_refl : reflexive ord.
Hypothesis ord_trans : transitive ord.
Hypothesis ord_total : total ord.
Hypothesis Pi0 : P i0.

Lemma extremumP : extremum_spec ord P F extremum.