proposition: Lemma edist_closel x y z : close x y -> edist (x, z) = edist (y, z).
proof: Proof. move=> /edist_closeP xy0; apply: le_anti; apply/andP; split. by rewrite -[edist (y, z)]add0e -xy0 edist_triangle. by rewrite -[edist (x, z)]add0e -xy0 [edist (x, y)]edist_sym edist_triangle. 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