Section RealDomainArgExtremum.
Context {I : finType} (i0 : I).
Context (P : pred I) (F : I -> R) (Pi0 : P i0).
Hypothesis F_real : {in P, forall i, F i \is real}.

Lemma real_arg_minP : extremum_spec <=%R P F [arg min_(i < i0 | P i) F i].