Definition Qlt_Qmax_lower_bound_r p q1 q2 (hyp:Qmax q1 q2 < p) := proj2 (Qlt_Qmax_lower_bound p q1 q2 hyp).

(* Specifications: *)
Lemma Qmin_involutive : forall q, Qmin q q = q.
Lemma Qmax_involutive : forall q, Qmax q q = q.
Definition Qmean (x y:Q):Q := (x+y) / (Qone + Qone).
Lemma Qmean_property:forall (x y:Q), x < y -> x < Qmean x y /\ Qmean x y < y.
Definition Qmean_property_l x y (hyp:x<y) := proj1 (Qmean_property x y hyp).