Definition P_Rmin_stt (P:R -> Prop) x y := Rmin_case x y P.#[deprecated(since="8.16", note="Use Rmin_case instead.")]
Notation P_Rmin := P_Rmin_stt.

(* Specifications: *)
Lemma exp_le_3 : exp 1 <= 3.
Lemma exp_neq_0 : forall x:R, exp x <> 0.
Theorem exp_increasing : forall x y:R, x < y -> exp x < exp y.
Theorem exp_lt_inv : forall x y:R, exp x < exp y -> x < y.
Lemma exp_ineq1 : forall x : R, x <> 0 -> 1 + x < exp x.
Lemma exp_ineq1_le (x : R) : 1 + x <= exp x.
Lemma ln_exists1 : forall y:R, 1 <= y -> { z:R | y = exp z }.
Lemma ln_exists : forall y:R, 0 < y -> { z:R | y = exp z }.