proposition: Lemma edist_pinfty_open : open [set xy : X * X | edist xy = +oo]%E.
proof: Proof. rewrite -closedC; have := edist_fin_closed; congr (_ _). by rewrite eqEsubset; split => z; rewrite /= ?ge0_fin_numE// ltey => /eqP. 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