Definition r_ub (h : TypeSpeed) : R := (h / rho_lb h)%R.Definition r_lb (h : TypeSpeed) : R := (h / rho_ub h)%R.

(* Specifications: *)
Lemma tan_lb_MaxBank_pos : (0 < tan_lb_MaxBank)%R.
Lemma tan_ub_MaxBank_pos : (0 < tan_ub_MaxBank)%R.
Lemma rho_lb_pos : forall h : TypeSpeed, (0 < rho_lb h)%R.
Lemma rho_pos : forall h : TypeSpeed, (0 < rho h)%R.
Lemma rho_ub_pos : forall h : TypeSpeed, (0 < rho_ub h)%R.
Lemma r_ub_0 : forall h : TypeSpeed, (r h < r_ub h)%R.
Lemma r_lb_0 : forall h : TypeSpeed, (r_lb h < r h)%R.
Lemma rho_PI2 : forall h : TypeSpeed, (rho h <= PI / 2)%R.
Lemma rho_strict_decreasing : forall h1 h2 : TypeSpeed, (h1 < h2)%R -> (rho h2 < rho h1)%R.
Lemma r_stric_increasing : forall h1 h2 : TypeSpeed, (h1 < h2)%R -> (r h1 < r h2)%R.