proposition: Lemma coarse_segment_monotone r x y: order r -> gle r x y -> sub (coarse (segment r x)) (coarse (segment r y)).
proof: Proof. by move=> or xy;move: (segment_monotone or xy) =>sm; apply: setX_Slr. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)