adherence value, extracted seq, limit point #1780
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affeldt-aist
added
the
enhancement ✨
affeldt-aist
commented
Nov 28, 2025
| Let A_nonempty x : A (N_ x) (idx_ x) !=set0. | ||
| Proof. by move: x => [[? ?]] []. Qed. | ||
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| Let elt_rel i j := [/\ (idx_ j = (idx_ i).+1), |
affeldt-aist
commented
Nov 28, 2025
| Qed. | ||
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| Let adherence_value_cvg_direct : adherence_value u_ a -> | ||
| exists2 f : nat -> nat, increasing_seq f & (u_ \o f @ \oo --> a). |
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Author
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Note that Bolzano-Weierstrass is a direct consequence of these lemmas. |
Tragicus
reviewed
Dec 3, 2025
| Qed. | ||
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| Definition adherence_value {R : numDomainType} (u_ : R^nat) (a : R) := | ||
| forall (e : R) n, e > 0 -> exists2 p, (p >= n)%N & `|u_ p - a| <= e. |
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I am wondering if we would prefer a \in closure (range u_ : set R^o).
Collaborator
How so? |
Co-authored-by: Quentin VERMANDE <[email protected]>
Co-authored-by: Quentin VERMANDE <[email protected]>
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Author
it just lacks a lemma to extract a sequence from a sequence with a finite image: |
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CHANGELOG_UNRELEASED.mdReference: How to document
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