Section ArgExtremum.
Context (I : finType) (i0 : I) (P : {pred I}) (F : I -> T) (Pi0 : P i0).
Hypothesis F_comparable : {in P &, forall i j, F i >=< F j}.
End ArgExtremum.
(* monotonicity *)

Lemma count_lt_ge x s : count (< x) s = size s - count (>= x) s.