Arguments real_ler_normlP {x y}.

(* Specifications: *)
Lemma real_eqr_norml x y :
x \is real -> (`|x| == y) = ((x == y) || (x == -y)) && (0 <= y).
Lemma real_eqr_norm2 x y :
x \is real -> y \is real -> (`|x| == `|y|) = (x == y) || (x == -y).
Lemma real_ltr_norml x y : x \is real -> (`|x| < y) = (- y < x < y).
Definition real_lter_norml := (real_ler_norml, real_ltr_norml).
Lemma real_ltr_normlP x y :
x \is real -> reflect ((-x < y) * (x < y)) (`|x| < y).