proposition: Lemma homo_lt_inj {disp disp' : unit} {T : orderType disp} {T' : orderType disp'} [f : T -> T'] : {homo f : x y / x < y >-> x < y} -> injective f.
proof: Proof. move=>fh x y fxy. case xy: (x == y); first by move:xy=>/eqP. by move:xy=>/negbT/lt_total/orP; case=>/fh; rewrite fxy lt_irreflexive. Qed.
imports: mathcomp(all_ssreflect ssrnum zmodp order constructive_ereal) preliminaries