#[deprecated(since="8.16",note="Use Rsqr_div'.")]
Notation Rsqr_div := Rsqr_div_depr.

(* Specifications: *)
Lemma Rsqr_eq_0 : forall x:R, Rsqr x = 0 -> x = 0.
Lemma Rsqr_minus_plus : forall a b:R, (a - b) * (a + b) = Rsqr a - Rsqr b.
Lemma Rsqr_plus_minus : forall a b:R, (a + b) * (a - b) = Rsqr a - Rsqr b.
Lemma Rsqr_incr_0 : forall x y:R, Rsqr x <= Rsqr y -> 0 <= x -> 0 <= y -> x <= y.
Lemma Rsqr_incr_0_var : forall x y:R, Rsqr x <= Rsqr y -> 0 <= y -> x <= y.
Lemma Rsqr_incr_1 : forall x y:R, x <= y -> 0 <= x -> 0 <= y -> Rsqr x <= Rsqr y.
Lemma Rsqr_incrst_0 : forall x y:R, Rsqr x < Rsqr y -> 0 <= x -> 0 <= y -> x < y.
Lemma Rsqr_incrst_1 : forall x y:R, x < y -> 0 <= x -> 0 <= y -> Rsqr x < Rsqr y.
Lemma Rsqr_neg_pos_le_0 : forall x y:R, Rsqr x <= Rsqr y -> 0 <= y -> - y <= x.
Lemma Rsqr_neg_pos_le_1 : forall x y:R, - y <= x -> x <= y -> 0 <= y -> Rsqr x <= Rsqr y.
Lemma neg_pos_Rsqr_le : forall x y:R, - y <= x -> x <= y -> Rsqr x <= Rsqr y.
Lemma neg_pos_Rsqr_lt : forall x y : R, - y < x -> x < y -> Rsqr x < Rsqr y.
Lemma Rsqr_bounds_le : forall a b:R, -a <= b <= a -> 0 <= Rsqr b <= Rsqr a.
Lemma Rsqr_bounds_lt : forall a b:R, -a < b < a -> 0 <= Rsqr b < Rsqr a.
Lemma Rsqr_abs : forall x:R, Rsqr x = Rsqr (Rabs x).
Lemma Rsqr_le_abs_0 : forall x y:R, Rsqr x <= Rsqr y -> Rabs x <= Rabs y.
Lemma Rsqr_le_abs_1 : forall x y:R, Rabs x <= Rabs y -> Rsqr x <= Rsqr y.
Lemma Rsqr_lt_abs_0 : forall x y:R, Rsqr x < Rsqr y -> Rabs x < Rabs y.
Lemma Rsqr_lt_abs_1 : forall x y:R, Rabs x < Rabs y -> Rsqr x < Rsqr y.
Lemma Rsqr_inj : forall x y:R, 0 <= x -> 0 <= y -> Rsqr x = Rsqr y -> x = y.
Lemma Rsqr_eq_abs_0 : forall x y:R, Rsqr x = Rsqr y -> Rabs x = Rabs y.
Lemma Rsqr_eq_asb_1 : forall x y:R, Rabs x = Rabs y -> Rsqr x = Rsqr y.
Lemma triangle_rectangle : forall x y z:R, 0 <= z -> Rsqr x + Rsqr y <= Rsqr z -> - z <= x <= z /\ - z <= y <= z.
Lemma triangle_rectangle_lt : forall x y z:R, Rsqr x + Rsqr y < Rsqr z -> Rabs x < Rabs z /\ Rabs y < Rabs z.
Lemma triangle_rectangle_le : forall x y z:R, Rsqr x + Rsqr y <= Rsqr z -> Rabs x <= Rabs z /\ Rabs y <= Rabs z.
Lemma Rsqr_inv' x : Rsqr (/ x) = / Rsqr x.
Lemma Rsqr_inv_depr : forall x:R, x <> 0 -> Rsqr (/ x) = / Rsqr x.