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fixes #1735 (adjacent_seq) #1745

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affeldt-aist merged 2 commits into from
Oct 31, 2025
Merged

fixes #1735 (adjacent_seq) #1745

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4a402fb
fixes #1735
affeldt-aist Oct 30, 2025
fe6f4c6
changelog
affeldt-aist Oct 30, 2025
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3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -339,6 +339,9 @@
+ `lb_ereal_inf` -> `le_ereal_inf_tmp`
+ `ereal_sup_ge` -> `le_ereal_sup_tmp`

- in `sequences.v`:
+ `adjacent` -> `adjacent_seq`

### Generalized

- in `pseudometric_normed_Zmodule.v`:
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6 changes: 4 additions & 2 deletions theories/sequences.v
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Expand Up @@ -57,7 +57,7 @@ From mathcomp Require Import ereal topology tvs normedtype landau.
(* is convergent and its limit is sup u_n *)
(* nonincreasing_cvgn u_ == if u_ is nonincreasing u_ and bound by below *)
(* then u_ is convergent *)
(* adjacent == adjacent sequences lemma *)
(* adjacent_seq == adjacent sequences lemma *)
(* cesaro == Cesaro's lemma *)
(* ``` *)
(* *)
Expand Down Expand Up @@ -681,7 +681,7 @@ rewrite -(opprK u_); apply: is_cvgN; apply/(@near_nondecreasing_is_cvgn _ (- m))
- by apply: filterS u_m => x u_x; rewrite lerNl opprK.
Qed.

Lemma adjacent (u_ v_ : R ^nat) : nondecreasing_seq u_ -> nonincreasing_seq v_ ->
Lemma adjacent_seq (u_ v_ : R ^nat) : nondecreasing_seq u_ -> nonincreasing_seq v_ ->
v_ - u_ @ \oo --> 0 ->
[/\ limn v_ = limn u_, cvgn u_ & cvgn v_].
Proof.
Expand All @@ -699,6 +699,8 @@ by split=> //; apply/eqP; rewrite -subr_eq0 -limB //; exact/eqP/cvg_lim.
Qed.

End sequences_R_lemmas.
#[deprecated(since="mathcomp-analysis 1.14.0", note="renamed to `adjacent_seq`")]
Notation adjacent := adjacent_seq (only parsing).

Definition harmonic {R : fieldType} : R ^nat := [sequence n.+1%:R^-1]_n.
Arguments harmonic {R} n /.
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