Section ExtremumIn.
Context {T : eqType} {I : finType} (ord : rel T).
Context (i0 : I) (P : pred I) (F : I -> T).
Hypothesis ord_refl : {in P, reflexive (relpre F ord)}.
Hypothesis ord_trans : {in P & P & P, transitive (relpre F ord)}.
Hypothesis ord_total : {in P &, total (relpre F ord)}.
Hypothesis Pi0 : P i0.

Lemma extremum_inP : extremum_spec ord P F (extremum ord i0 P F).