proposition: Lemma nbhs_left_gt x z : z < x -> \forall y \near x^'-, z < y.
proof: Proof. move=> xz; rewrite nbhs_left0P; near do rewrite -ltrN2 opprB ltrBlDl. by apply: nbhs_right_lt; rewrite subr_gt0. Unshelve. all: by end_near. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule