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 lcomparable_ltgtP x y : x >=< y ->
comparel x y (min y x) (min x y) (max y x) (max x y)
(y `&` x) (x `&` y) (y `|` x) (x `|` y)
(y == x) (x == y) (x >= y) (x <= y) (x > y) (x < y).