proposition: Lemma pinfty_ex_gt (m : R) (A : set R) : m \is Num.real -> (\forall k \near +oo, A k) -> exists2 M, m < M & A M.
proof: Proof. move=> m_real Agt; near (pinfty_nbhs R) => M. by exists M; near: M => //; apply: nbhs_pinfty_gt. 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