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}.
End RealDomainArgExtremum.
(* norm *)

Lemma real_ler_norm x : x \is real -> x <= `|x|.