proposition: Lemma in_segmentDgt0Pl x y z : reflect (forall e, e > 0 -> y \in `[(- e + x), (e + z)]) (y \in `[x, z]).
proof: Proof. apply/(equivP (in_segmentDgt0Pr x y z)). by split=> zxy e /zxy; rewrite [z + _]addrC [_ + x]addrC. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(div fintype bigop order ssralg finset fingroup) mathcomp(ssrnum)